Re: how you you express this?
The observed frequency in the past is 100%.
To estimate a future probability, you have to consult your prior beliefs. For example, if you watched the sun rise 20 days in a row, you might feel that the chance it would rise tomorrow was 99.999999%. On the other hand, if you watched 20 roulette spins that resulted in a number other than 5, it wouldn't be likely to chance your belief that there is 37/38 chance of getting a number other than 5.
One way to express prior belief is with numbers a and b. If you observe 20 out of 20 successes, you estimate the future probability as (20+a)/(20+b). That means before you observed anything, you thought the probability was a/b. If a and b are large, you had a lot of prior information relative (as in the roulette case). If a and b are small, you didn't know much before you made observations. That might be the case if you were trying something new.
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