In chapter 10, Samuel finally comes out and tells Saul plainly that he is to be the king of Israel, and he anoints him with oil. (I've always thought this a strange practice, and probably ought to read up on it more. I can't imagine having a jar of oil dumped on your head is a pleasant thing, but I suppose I'm missing something.) He tells him a series of signs that will come to pass to verify to him that all he has spoken is true. After seeing the signs, Saul is to go to Gilgal, where something important is to occur.
So Saul comes along the road and meets some prophets, and immediately, the Spirit of God comes over him and he begins to prophesy as well. People see him there and ask in amazement, "Is Saul also among the prophets?" This is an interesting story for many reasons, one of which is that it occasions the skeptic to ask, as the SAB does, how can this story and the similar one in 1Samuel 19 both be true? Actually, the SAB flat out denies that they can both be true, but I fail to see why. Certainly, if we accept that such a thing could happen once, it could happen again many years later. The problem is not the repetition of action, but the ascribing of the "proverb" to both events, right? But why should that be a problem? Sure, it's strange, but why should it not be a possibility that the first event made some people say such a thing, and the second event made it all the more popular?*
The thing that makes it very interesting is the realization that this event is a miraculous moment in which Saul loses control of himself that was engineered to verify God's will that Saul be made king. The second event is, on the other hand, a miraculous moment in which Saul loses control of himself that was engineered to verify God's will that Saul be deposed as king. God has a sense of humor, I have no doubt about that.
Saul returns home and tells his uncle that he met Samuel, but not that Samuel said anything about the political situation to be. It's interesting that Saul, upon returning home, has a lengthy conversation with his uncle rather than his father. Perhaps there is something in the structure of Saul's family we are not being told that might explain the trouble of the previous chapter?
Samuel calls all the people together and gives them one last lecture on how bad they are for wanting a king, and then makes a choice. The selection process seems very odd, and not a lot of detail is given, but eventually, Saul is chosen to be king, although nobody can find him, because he's hiding for some unnamed reason. They bring him out, and everyone is impressed, because he's a tall handsome guy.
The SAB notes the writing in verse 25 as a "lost book of the Bible", which I think is an overstatement of the idea being put forth here. "Book" is pretty much a catch-all term for anything written down, and I've always assumed that what has happened here is Samuel has written up a short scroll with the details of the rules in the Mosaic Law that the king should be especially aware of, like Deuteronomy 17, which has a handful of laws concerning kingship. Whatever it was, it seems likely that this is more of a "lost pamphlet of the Bible".
In the last verse of this chapter, we are told that there were a few people in the crowd ("children of Belial", generally a term for particularly sinful people) who didn't think highly of the idea of Saul. The SAB finds this absurd, but I don't know why. Once again, I seem to be missing the point. I probably would have felt the same way, but perhaps it's something about the wording? I'm missing what the issue is here.
*Robert Alter says in his footnotes on chapter 19, "The doublet, far from being a stammer of transmission or inept or automatically inclusive redaction, is vividly purposeful, providing a strong frame for Saul's painful story. ... To the ancient audience, however, the recurrence would not have seemed a contradiction, and the conflicting valences given to the explanation of the proverbial saying add to the richness of the portrait of Saul, formally framing it at beginning and end."