As a general rule, it's safe to use "may" for permission and "might" for possibility. There is some crossover and not everyone makes the distinction (in fact, "might" used to commonly be used for permission) but you won't be wrong if you use them that way. It's nothing to do with anything being likely or less likely.
It might have rained.
She might have broken the glass.
Might she have broken the glass?
Might it have been the cat that smashed the vase?
May I go to the bathroom?
Yes, you may.
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