So Solomon expelled Abiathar from being priest to the LORD, thus fulfilling the word of the LORD that he had spoken concerning the house of Eli in Shiloh.
Abiathar and Joab were equally guilty of treason, yet Solomon rightly made a difference: Abiathar is only degraded and confined to Anathoth, spared because he had borne the ark before David and suffered all his afflictions. Kindness to God's people shall be remembered to their advantage.
AI summary
Commenting on 1 Kings 2:26-34
Then tidings came to Joab,.... Of the death of Adonijah, and the deposition of Abiathar: for Joab had turned after Adonijah; publicly appeared at his feast, when he was saluted king by him, and others, and privately gave him advice in the affair of Abishag: though he turned not after Absalom; did not join with him in his rebellion, but faithfully adhered to David; and...
So Solomon thrust out Abiathar - This was for having taken part before with Adonijah, but by it a remarkable prophecy was fulfilled; see 1 Samuel 2:13-35 (note), and the notes there. God had told Eli that the priesthood should depart from his house; Abiathar was the last of the descendants of Ithamar, of which family was Eli the high priest.