Luke 1

Most scholars believe Luke was a gentile convert to the gospel after the Savior's death and resurrection.  As Luke begins his record, he tells Theophilus concerning -

"...those things which are most surely believed among us,

2 Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word..."  (New Testament | Luke 1:1 - 2)

It seems apparent to me that in order to provide an accurate record of the Savior and gospel they so readily believed, that Luke interviewed eyewitnesses and those that ministered the word. Because of the that, Luke records the birth of John the Baptist and the Savior.

It is my personal belief that the "eyewitness" that shares the events of these two conceptions and births was Mary, the mother of Jesus.  Why would I make such a bold statement, because Luke records of the Savior's birth -

"...Mary kept all these things, and pondered them in her heart."  (New Testament | Luke 2:19)

I can just picture in my mind, Mary revealing this history to Luke telling him that she had kept all these things and not shared them.

The general population may had known the story of Zacharias, but Mary would have known these facts of Elizabeth.