Samuel was willing to hide his knowledge that Saul had been chosen by God and instead he allowed God to reveal his will through his appointed means. Samuel refused to take credit for the discovery of Saul. It would have been easy for him to have recounted his previous meeting with Saul and used this to present himself in a favourable way. But instead he went through the process that God had set up in Israel. The determination not to draw attention to himself is a good mark of a servant of God.
Samuel also refused the possibility of manipulation of events. Perhaps he now realised his own mistake in appointing his sons to an office they were unfit to hold. In any case, he did not try and arrange events.
This incident is a further reminder that God does not need our intervention to bring to pass the appointments he has in mind and this should stimulate confidence in his providential control of affairs.