The combination of the high priest, the prophet, and the captain of the bodyguard (the Cherethites and Pelethites, 1 Kings 1:38), would show the people that the proceedings had the king’s sanction. The order of the names marks the position of the persons with respect to the matter in hand.
Related Commentaries of 1 Kings 1:32
1 Kings 1:32
32 And king David said, Call me Zadok the priest, and Nathan the prophet, and Benaiah the son of Jehoiada. And they came before the king.