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.)
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.