Referring to the Gospel of Matthew, the number of "Wise Men" or "Magi" is not named. However, it is traditionally assumed to be three because of the three gifts (frankincense, myrrh & gold) that were given at that time. Church Father Origen (185-224 ad) was the first to denote the "three" Magi in his writings.
Likewise, the notion of "Kings"(*) is a traditional development, but also seems to have some basis, as derived from Psalms 71:10, where the prophecy of the coming Christ is said to have been denoted:

[The kings of Tharsis and the islands shall offer presents: the kings of the Arabians and of Saba shall bring gifts: ] -Psalms 71:10

(*) It was Tertullian (c.160-230) ]who first spoke of the three Magi as kings ("Adv. Marcion.", III, xiii), referring to Psalms (67:30, 71:10) and to Isaiah (60:3): "kings [shall come] to the brightness of thy rising". "Ille magi reges sunt [ these Magi are indeed kings ]," St Caesarius of Arles stressed in the sixth century.

Regardless, in view of a literal interpretation of the New Testament, neither "Three" or "Kings" appear in the Gospel story. However, it is important to point out that even though these points are missing in the literal interpretation, the custom of such inclusion is widely denoted across the world.
In fact, a shrine even exists at the Cologne Cathedral which claims to have the remains of the "Three" Wise Men.

Why is this so? If the bible does not denote these things exactly, then why is it traditionalized as such? Why the "Three Kings"?

In part, it would seem that these notions were set in motion by church fathers such as Origen and Tertullian. However, if one steps back to examine the pagan mythological tradition that preceded Christianity ( which Origen and Tertullian were very aware of ), the 'traditional' notion of there being "Three Kings", rather than an unknown number of "Magi / Wisemen" comes more clear, as these literary characteristics existed in other saviors of paganism.

Going back the scripture in question, Matthew reads:
"Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem, Saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him."
-Matthew 2:1-2
" . . and lo, the star, which they had seen in the East went before them, till it came to rest over the place where the child was"
-Matthew 2:9

The underlying summery paraphrased here is:
'Jesus had a birth star in the east, and the Wise Men used the star to locate the King of the Jews (Jesus)'

Now- are their any pre-Christian religious traditions that denote the same idea? If there are, then the characteristics of the prior tradition(s) was, in all odds, an influence and thus the ramifications of those characteristics would carry over as well.

The answer is yes, as B. Walker points out in regards to the Osirus/Horus myth of Ancient Egypt:

"Osiris's coming was announced by Three Wise Men: the three stars Mintaka, Anilam, and Alnitak in the belt of Orion, which point directly to Osiris's star in the east, Sirius (Sothis), significator of his birth..."

[ Walker, Barbara: The Womans Encyclopedia of Myths and Secrets, Harper, p748-754 ]

And as Massey elaborates:

[ Massey, Gerald: The Historical Jesus and the Mythical Christ, Book Tree, 1883, p12-13 ]

In conclusion, the notion of the 'Three Kings' visiting Jesus after following his birth star is, in fact, an astronomical allegory that was a part of the Egyptian mythology prior to the advent of Christianity. Even though the Bible does not denote 'Three' or 'Kings' exactly, the traditional, pagan nature of it is obvious... which also explains why the tradition of 'Jesus visited by the Three Kings' is so widespread today.