The surprise comes only to those that try to overload probability with roles it should not have. For example "A implies B" does imply P(B|A)=1 but P(B|A)=1 doesn't imply "A implies B". While it is common that if we know systematically that a certain probability is high it is a promising line of argument for causations and implications it doesn't always carry through (meta-example I am in essence arguing that while an okayish rule of thump, it is actually improper to infer causations from probabilities. I am doing this by pointing out that P(causation|probability) ~ 1 and P(causation|probability)<1 which alone is only suggestive that it is so (or the actual steps are implied)).
but P(B|A)=1 doesn't imply "A implies B".
Can you give a counterexample?
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