There is no good definition of probability. For frequentists, it requires an infinite number of independent events, i.e., it doesn’t exist in the real world. For Bayesians, it’s subjective, i.e., arbitrary and useless for science.
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Wittgenstein pointed out that there's no good definition for anything. It's fascinating because it points to a naturalistic origin to various intuitions. Why would evolution gift us an intuition of probability that is logically water-tight? (It's also a clue to strong ai)
Most people find probability extremely unintuitive. And the problems with the existing definitions are well known.
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I would say most people have a wrong intuition of probability. Thus mixing up conditionals and marginals. Or getting the conditional the wrong way. Or trying to find links between independent events. We have a strong intuition on probability but more often than not it is wrong.
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Oh, this is absolutely true. But it's also not true. It depends on how the information is presented. Your below average person has no trouble with conditional/marginals if you provide them as numbers. (1000 people, 200 do this, etc.) There's peer reviewed liturature on this.
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