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One needs to keep in mind that a lot of the time, "correct" probability is either very close to 0 or very close to 1, you just can't figure out which because of limited computing time. It does feel like you should use probability that's somewhere in the middle in those cases, but a: there's no formalism for doing so, and even more devastatingly, b: spending time on consistent probabilities leaves less time for actual simulation, inference, or what ever it is that you do to find if its very close to 1 or very close to 0.
Remember, that by the Bayesian formulation of probability, there is no such thing as the "correct" probability. All probabilities are conditional on your personal knowledge. Using frequentist language like you are just muddles up the issue. If you had written your post in the Bayesian formulation, your point would be trivial. (And that, by the way, is the argument for using the Bayesian formulation and not the frequentist one.)
Often, you do have enough knowledge to get to something close to 1 or close to 0, you just can't run the computation because its too expensive.