John Chrysostom

The word of God here mentioned was a commandment, for the son of Zacharias came not of himself, but God moved him.

Catena Aurea by Aquinas ↗

Theophylact of Ohrid

"The word of God came to John," it is said, so that you would know that he came to bear witness about Christ not as a self-appointed man, but because he was moved by the Spirit of God. By "word" understand either the Holy Spirit or the commandment of God. The word of God came to John "in the wilderness." Since the children of the forsaken church, that is, the church from the Gentiles, were more numerous than the children of "her who has a husband" (Isa. …

Commentary on Luke ↗

Bede

During the high priesthood of Annas and Caiaphas, the word of the Lord came to John, the son of Zechariah, in the desert. Both indeed, at the beginning of John's prophecy, that is, Annas and Caiaphas were the chief priests; but Annas held the office for that year, while Caiaphas administered it in the year when the Lord ascended the cross, and indeed with three others in between completing the pontificate, but especially with those mentioned by the evangelist who were related to the passion of the Lord. …

On the Gospel of Luke ↗

Bonaventure

As for the division of the priesthood, there is added: Under the high priests Annas and Caiaphas, who, moved by ambition, as Bede says, were purchasing the high priesthood from the Romans. Whence, because according to Bede and Josephus priests were no longer being instituted through anointing but through earthly power, therefore the priestly anointing and the royal anointing had ceased. …

Commentary on Luke, Chapter 3 ↗