When you know something but can't justify it to yourself.

[robvalue]

Listening to your intuition can be the justification. We're not always able to consciously think everything through, with so much going on, and so many past experiences to relate to. Sometimes we don't have time to sit down and work everything through. And especially if our intuition is telling us to play it on the safe side (don't say something possibly offensive, don't go down that dark alleyway) then there's usually little risk in taking the "advice".

Of course, following intuition for more formal inquiries is generally a bad idea, except as a starting point. I also don't feel comfortable that I "know" something unless I can justify it with evidence to myself. This is usually evidence that I think another reasonable person would accept.

Another question is how important is the belief? Does it have any impact or significance? If not, then worrying about it is probably wasted effort