Numeric representation may be the same[0], but the rules of how to do math on them, and what that math means, are different.
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[0] - AFAIK dealing with Bayesian math, it's usually more useful to take a logarithm of all probabilities, so you can add them instead of multiplying. This translation expands the range from <0, 1> to <-infinity, +infinity>, and incidentally makes it clear why some people say that "zero and one are not probabilities".
Comments
Numeric representation may be the same[0], but the rules of how to do math on them, and what that math means, are different.
--
[0] - AFAIK dealing with Bayesian math, it's usually more useful to take a logarithm of all probabilities, so you can add them instead of multiplying. This translation expands the range from <0, 1> to <-infinity, +infinity>, and incidentally makes it clear why some people say that "zero and one are not probabilities".
`log(x)` does not give `+inf` on the range `(0,1)`, I think you're thinking of "log odds" aka a "logit" which is `log(x/(1-x))`