how probabilities of events feel like

Gut feelings have pretty bad resolution. In particular, I don't think gut feelings can differentiate between, say, 2% and 3%.

As a rough approximation (and, possibly, subject to the typical mind fallacy :-D), I think the gut thinks in these categories, assuming the probability is of something bad happening:

• Too low-probability to even think about it.
• Too low-probability to worry about it unless the consequences are really bad.
• Not likely, but worrisome -- worth guarding against unless prevention is expensive/unpleasant.
• Feels dangerous, there is motivation to do something about it.
• It's coming my way, active measures are called for.
• I'm fucked.

For fine resolution you can train your mind. I'm not sure how trainable your gut is.