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 righteous in the sight of God, observing all the Lord’s commands and decrees blamelessly. 7 But they were childless because Elizabeth was not able to conceive, and they were both very old.
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 call him John.
What was Zechariah's prayer? One easy guess would be that he was praying for a son, but verse 7 states that his wife was barren and that both were very old, so by this point, why would Zechariah still be hoping or praying for a son? His prayer could also have been something else and God just chose to give him a son as something like a bonus, or a reward, or a gift. At a shallow reading, there don't really seem to be any clues as to what Zechariah's prayer was.
Hence, I'm asking: is there any tradition or exegesis from any branch of Christianity that states what Zechariah's prayer was? If there is a small number of different traditions, please list them together in one answer. If there are somehow a large number of different traditions, please say so and give the most widespread/mainstream ones. I expect that there'll be at least a Catholic tradition and/or an Orthodox tradition.