How did the Three Kings know when to come to Bethlehem?

This question, no doubt, refers to the magi who the Gospel According to St Matthew says followed a star to see the baby Jesus.

The Latin Word magi (sing: magus) meant the priests of the Zoroastrian god, Ahura Mazda ("Wise Lord"). Matthew was portraying the priests of this great religion as regarding the birth of a Jewish Messiah as a momentous event. By having them wish to worship him, Matthew was probably demonstrating that Jesus had dominion over even the Zoroastrians. In later centuries, the Zoroastrian connection became less important and the terms "wise men" or even "kings" tend to be used in English translations.

In the Gospel According to St Matthew, wise men saw a star in the east and believed that it heralded a new king, who they somehow knew would be in Judea. They went to Jerusalem, which means that the star did not actually lead them to Bethlehem. King Herod told them to look in Bethlehem, where they found the baby Jesus.

However, the author of the the Gospel According to St Luke knew nothing of the story of the wise men visiting Jesus, but had poor shepherds visit him instead. Dr Rowan Williams, the former Archbishop of Canterbury and leader of the world's Anglicans, has described the story of the three wise men as nothing but a "legend" and says there is little evidence that they existed.