Jamieson, Fausset and Brown on 1 Samuel 16:11

11. There remaineth yet the youngest, and, behold, he keepeth the sheep--Jesse having evidently no idea of David's wisdom and bravery, spoke of him as the most unfit. God, in His providence, so ordered it, that the appointment of David might the more clearly appear to be a divine purpose, and not the design either of Samuel or Jesse. David having not been sanctified with the rest of his family, it is probable that he returned to his pastoral duties the moment the special business on which he had been summoned was done.