There weren't 3, but it is the same "tradition" mindset to say 12. The bible doesn't give a number, so we need not apply one. All of Jerusalem of in a stir over them, so however many there were, it was enough to get a city's attention.
They showed up when he was closer to 2 years old, and to his HOUSE, they did NOT show up to the manger.
Lastly, these men knew the bible. They weren't blindly following a star (which has a number of possible meanings, by the way) but rather they saw signs that pointed to the birth of the biblically promised King... which meant they knew the bible. Since these men came from the same area Judah had been captive in, it is very possible if not likely they were descendants of those Daniel taught, or... we members of Judah (Jews) who didn't come home when Judah left the Babylonian (Persian by that time) captivity.