Jamieson, Fausset and Brown on 1 Kings 1:7

7. he conferred with Joab--The anxiety of Adonijah to secure the influence of a leader so bold, enterprising, and popular with the army was natural, and the accession of the hoary commander is easily accounted for from his recent grudge at the king (see on 2Sa 19:13).

and with Abiathar the priest--His influence was as great over the priests and Levites--a powerful body in the kingdom--as that of Joab over the troops. It might be that both of them thought the crown belonged to Adonijah by right of primogeniture, from his mature age and the general expectations of the people (1Ki 2:15).