Knowing it's correct. You've just instructed it not to guess remember? With practice people can get really good at guessing all sorts of things.
I think people have a serious misunderstanding about how these things work. They don't have their training set sitting around for reference. They are usually guessing. Most of the time with enough consistency that it seems like they "know'. Then when they get it wrong we call it "hallucinations". But instructing then not to guess means suddenly they can't answer much. There no guessing vs not with an LLM, it's all the same statistical process, the difference is just if it gives the right answer or not.