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.

And King David said, call me Zadok the priest,.... Not Abiathar the high priest, for he had joined Adonijah; and besides Zadok was David's favourite priest, and for him the high priesthood was designed, as it was in a little time translated to him:

and Nathan the prophet; who very probably went out of the room when Bathsheba was called in: and

Benaiah the son of Jehoiada; the captain of his guards:

and they came before the king; who it is very likely sat up in his bed, and they stood around him.

David then sent for Zadok, Nathan, and Benaiah, and directed them to fetch the servants of their lord (אדניכם, a pluralis majestatis, referring to David alone), and to conduct Solomon to Gihon riding upon the royal mule, and there to anoint him and solemnly proclaim him king. The servants of your lord (אדניכם עבדי) are the Crethi and Plethi, and not the Gibborim also (Thenius), as 1 Kings 1:38 clearly shows, where we find that these alone went down with him to Gihon as the royal body-guard. לי אשׁר על־הפּרדּה, upon the mule which belongs to me, i.e., upon my (the king's) mule. When the king let any one ride upon the animal on which he generally rode himself, this was a sign that he was his successor upon the throne. Among the ancient Persians riding upon the king's horse was a public honour, which the king conferred upon persons of great merit in the eyes of all the people (cf. Esther 6:8-9). פּרדּה, the female mule, which in Kahira is still preferred to the male for riding (see Rosenmller, bibl. Althk. iv. 2, p. 56). Gihon (גּחון) was the name given, according to 2 Chronicles 32:30 and 2 Chronicles 33:14, to a spring on the western side of Zion, which supplied two basins or pools, viz., the upper watercourse of Gihon (2 Chronicles 32:30) or upper pool (2 Kings 18:17; Isaiah 7:3; Isaiah 36:2), and the lower pool (Isaiah 22:9). The upper Gihon still exists as a large reservoir built up with hewn stones, though somewhat fallen to decay, which is called by the monks Gihon, by the natives Birket el Mamilla, about 700 yards W.N.W. from the Joppa gate, in the basin which opens into the valley of Hinnom. The lower pool is probably the present Birket es Sultan, on the south-western side of Zion (see Robinson, Palestine, i. p. 485ff., 512ff., and Biblical Researches, p. 142ff.). The valley between the two was certainly the place where Solomon was anointed, as it is not stated that this took place at the fountain of Gihon. And even the expression גּחון על אתו הורדתּם (take him down to Gihon) agrees with this. For is you go from Zion to Gihon towards the west, you first of all have to descend a slope, and then ascend by a gradual rise; and this slope was probably a more considerable one in ancient times (Rob. Pal. i. p. 514, note).

(Note: The conjecture of Thenius, that גּחון should be altered into גּבעון, is hardly worth mentioning; for, apart from the fact that all the ancient versions confirm the correctness of גּחון, the objections which Thenius brings against it amount to mere conjectures or groundless assumptions, such as that Zadok took the oil-horn out of the tabernacle at Gibeon, which is not stated in v. 39. Moreover, Gibeon was a three hours' journey from Jerusalem, so that it would have been absolutely impossible for the anointing, which was not commanded by David till after Adonijah's feast had commenced, to be finished so quickly that the procession could return to Jerusalem before it was ended, as is distinctly recorded in v. 41.)

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.

1Ki 1:32-49. Solomon, by David's Appointment, Is Anointed King.

1:32-53 The people expressed great joy and satisfaction in the elevation of Solomon. Every true Israelite rejoices in the exaltation of the Son of David. Combinations formed upon evil principles will soon be dissolved, when self-interest calls another way. How can those who do evil deeds expect to have good tidings? Adonijah had despised Solomon, but soon dreaded him. We see here, as in a glass, Jesus, the Son of David and the Son of God, exalted to the throne of glory, notwithstanding all his enemies. His kingdom is far greater than that of his father David, and therein all the true people of God cordially rejoice. The prosperity of his cause is vexation and terror to his enemies. No horns of the altar, nor forms of godliness, nor pretences to religion, can profit those who will not submit to His authority, and accept of his salvation; and if their submission be hypocritical, they shall perish without remedy.