Snap all in against all his trip K's. Why do you even ask if you are a 88% favorite and you think he will call your all-in? Or if you think he won't call an all-in, just keep raising smaller, whatever you think is best to get all your money in the pot.
A tiny % of the time he will hit his 3 outer or have KK, but so what?
His raise size to $0.56 is ridiculous, he might do that because he is wary of your raise, so don't go all in yet, raise smaller or even just call if you think he won't call a further raise.
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