Eliezer_Yudkowsky comments on Explainers Shoot High. Aim Low! - Less Wrong
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An important transformation of probabilities is the log odds, the logarithm of the odds ratio of the probability, log(p/(1-p)). This has the advantage that you can simply add the log-likelihood to your log-odds prior to get the revised probability. Bayes becomes addition.
In the log odds, 1 comes out as positive infinity and 0 comes out as negative infinity.
Negative and positive infinity are not real numbers, and 0 and 1 are not probabilities.