Christian view of why there are so many similarities between Quran and Bible?

Your question, "How did the prophet, Muhammad, know about this if it was not revealed by God," is really an argument from incredulity[1]. You can't (or haven't) imagined a different explanation, so you assume there isn't one.

That said, the simplest possible explanation I can think of is that all of these cultures share a historical and mythological background:

Although it mostly died out 1600 to 1700 years ago, Mesopotamian religion has still had an influence on the modern world, predominantly because Biblical mythology that is today found in Judaism, Christianity, Islam and Mandeanism shares some overlapping consistency with ancient Mesopotamian myths, in particular the Creation Myth, the Garden of Eden, The Great Flood, Tower of Babel and figures such as Nimrod and Lilith (the Assyrian Lilitu). In addition the story of Moses' origins shares a similarity with that of Sargon of Akkad, and the Ten Commandments mirror Assyrian-Babylonian legal codes to some degree. It has also inspired various contemporary Neopagan groups to begin worshipping the Mesopotamian deities once more, albeit in a way often different from that of the Mesopotamian peoples.[2]

[1] http://rationalwiki.org/wiki/Argument_from_incredulity

[2] http://en.wikipedia.org/wiki/Religion_in_Mesopotamia

Muhammad had most likely been in contact with Christian and Jewish influences

As a child/young man, Muhammad, whilst traveling on trading missions with his uncle to Syria, would have no doubt come into direct contact with Christians and Jews, or at the very least those who knew the traditions of those two religions in that part of the world at that time.

In fact Muhammad, according to many histories, was supposed to have met a Nestorian monk, named Waraqah ibn Nawfa, on one of these trips who predicted that Muhammad would become a great prophet.

So even according to Islamic traditions and as the life of Muhammad himself shows, Muhammad and his contemporaries would have had plenty of knowledge of and contact with these other religions.

Now, you could make argument for or against the observation that the similarities are so great that even with contact, an illiterate merchant would not have been able produce so similar a reproduction without divine intervention. I am not arguing for or against that here, only that Muhammad was not operating within a total cultural or historical vacuum in that region, at the time in history.

Prepare for your mind to be blown

Mohammedanism was a heresy: that is the essential point to grasp before going any further. It began as a heresy, not as a new religion. It was not a pagan contrast with the Church; it was not an alien enemy. It was a perversion of Christian doctrine. It vitality and endurance soon gave it the appearance of a new religion, but those who were contemporary with its rise saw it for what it was_not a denial, but an adaptation and a misuse, of the Christian thing. It differed from most (not from all) heresies in this, that it did not arise within the bounds of the Christian Church. The chief heresiarch, Mohammed himself, was not, like most heresiarchs, a man of Catholic birth and doctrine to begin with. He sprang from pagans. But that which he taught was in the main Catholic doctrine, oversimplified. It was the great Catholic world on the frontiers of which he lived, whose influence was all around him and whose territories he had known by travel which inspired his convictions. He came of, and mixed with, the degraded idolaters of the Arabian wilderness, the conquest of which had never seemed worth the Romans' while.

Hilare Belloc - The Great Heresies Chapter 4

Belloc's book on the great heresies is the only place I've ever read this; that Islam is in fact a heresy of Catholicism. But it makes sense (and if someone knows of a good refutation, I'd like to read it), especially in light of your question. So, you either believe this or you don't because not only does Islam have the same roots as Judaism and Christianity, Muslims truly worship the same one God (from a philosophical standpoint, if there's only one, it's gotta be Him right?).

So, the doctrinal differences that Belloc points out are:

1. The Incarnation (That God could be made man)
2. The Trinity (The God is three persons)
3. The priesthood and Sacraments (That invisible things can be made real by human help)

Different heresies through all the years of Our Lord have held similar beliefs, but only Islam held them all and retained the same God. Some Islamic scholars even preserved the meta-physical tradition of Aristotle which made its way from St. Augustine to St. Thomas Aquinas by way of Averroes. So, Catholic theology and philosophy are linked to Islam (or at least through Islam) and that's not a bad thing.

What was a bad thing was Islam was taking over Christian lands and souls by force.

And that made all the difference. Folks, like Tertullian would say,

the blood of the martyrs is the seed of the Church

and it would be difficult to say that about Islam, you might say, the blood of other people is the seed of Islam. Although certainly quite a few people were convinced for other reasons and those reasons might include the fact that Islam sounded familiar, but it didn't have the seemingly extraneous fancy stuff you find in the Catholic Church and that made it more palatable to desert folks who couldn't find the time for all the feasting.

But beyond that, it's pretty natural that conquered and unconquered people (in Spain and modern day Turkey) would share a lot of their culture. Northern Africa, Ethiopia, the Holy Land contained plenty of Christians prior to 600 and it took quite a long time for them to be converted.

Another "historical approach" remark - there were some Christians in Arabia in Muhammad's times, so even if Muhammad was illiterate, he could ask some of his Christian neighbors and listen to the stories. But most of these "Christians" were not orthodox and many of them belonged to sects today refered to as gnostics, not Christians. Bible as we know it wasn't recognized as Holy Spcripture by all of them, and translations of Bible were rare and often poor. This explains many refences to Childhood Gospel and other apocryphas (for example creation of the birds by child Jesus) in Quran, and also some statements that originated in misunderstanding Bible. For example in Bible John the Baptist was first of this name in his family, but in Quran Yahya (John the Baptist) was the first of this name in general (from all mankind). Muhammad simply knew some second-hand "Bible stories", and we won't find out who originally misunderstood them.

Of course, some old testament stories might have survived in Arabic culture since Abraham.

EDIT - some sources from both holy writs to back up my example with John the Baptist:

Luke 1:5-25

5 In the time of Herod king of Judea there was a priest named Zechariah, who belonged to the priestly division of Abijah; his wife Elizabeth was also a descendant of Aaron. 6 Both of them were upright in the sight of God, observing all the Lord’s commandments and regulations blamelessly. 7 But they had no children, because Elizabeth was barren; and they were both well along in years.

8 Once when Zechariah’s division was on duty and he was serving as priest before God, 9 he was chosen by lot, according to the custom of the priesthood, to go into the temple of the Lord and burn incense. 10 And when the time for the burning of incense came, all the assembled worshipers were praying outside.

11 Then an angel of the Lord appeared to him, standing at the right side of the altar of incense. 12 When Zechariah saw him, he was startled and was gripped with fear. 13 But the angel said to him: “Do not be afraid, Zechariah; your prayer has been heard. Your wife Elizabeth will bear you a son, and you are to give him the name John. 14 He will be a joy and delight to you, and many will rejoice because of his birth, 15 for he will be great in the sight of the Lord. He is never to take wine or other fermented drink, and he will be filled with the Holy Spirit even from birth. 16 Many of the people of Israel will he bring back to the Lord their God. 17 And he will go on before the Lord, in the spirit and power of Elijah, to turn the hearts of the fathers to their children and the disobedient to the wisdom of the righteous—to make ready a people prepared for the Lord.”

18 Zechariah asked the angel, “How can I be sure of this? I am an old man and my wife is well along in years.”

19 The angel answered, “I am Gabriel. I stand in the presence of God, and I have been sent to speak to you and to tell you this good news. 20 And now you will be silent and not able to speak until the day this happens, because you did not believe my words, which will come true at their proper time.”

21 Meanwhile, the people were waiting for Zechariah and wondering why he stayed so long in the temple. 22 When he came out, he could not speak to them. They realized he had seen a vision in the temple, for he kept making signs to them but remained unable to speak.

23 When his time of service was completed, he returned home. 24 After this his wife Elizabeth became pregnant and for five months remained in seclusion. 25 “The Lord has done this for me,” she said. “In these days he has shown his favor and taken away my disgrace among the people.”

And luke 1:57-66

57 When it was time for Elizabeth to have her baby, she gave birth to a son. 58 Her neighbors and relatives heard that the Lord had shown her great mercy, and they shared her joy.

59 On the eighth day they came to circumcise the child, and they were going to name him after his father Zechariah, 60 but his mother spoke up and said, “No! He is to be called John.”

61 They said to her, “There is no one among your relatives who has that name.”

62 Then they made signs to his father, to find out what he would like to name the child. 63 He asked for a writing tablet, and to everyone’s astonishment he wrote, “His name is John.” 64 Immediately his mouth was opened and his tongue was loosed, and he began to speak, praising God. 65 The neighbors were all filled with awe, and throughout the hill country of Judea people were talking about all these things. 66 Everyone who heard this wondered about it, asking, “What then is this child going to be?” For the Lord’s hand was with him.

And the extract from this in Quran (Surah 19 - Maryam, verses 2-10):

[This is] a mention of the mercy of your Lord to His servant Zechariah

When he called to his Lord a private supplication.

He said, "My Lord, indeed my bones have weakened, and my head has filled with white, and never have I been in my supplication to You, my Lord, unhappy.

And indeed, I fear the successors after me, and my wife has been barren, so give me from Yourself an heir

Who will inherit me and inherit from the family of Jacob. And make him, my Lord, pleasing [to You]."

[He was told], "O Zechariah, indeed We give you good tidings of a boy whose name will be John. We have not assigned to any before [this] name."

He said, "My Lord, how will I have a boy when my wife has been barren and I have reached extreme old age?"

[An angel] said, "Thus [it will be]; your Lord says, 'It is easy for Me, for I created you before, while you were nothing.' "

[Zechariah] said, "My Lord, make for me a sign." He said, "Your sign is that you will not speak to the people for three nights, [being] sound."

I see nothing really new in the Quran version, just omission of many details, and changes concerning the time Zechariah couldn't speak and the detail with previous Johns. This name was definitely not unknown in Izrael before (I remember one John in the Maccabean books, and I don't think he's the only one mentioned in Old Testament).