This question already has an answer here:
If I get $s$ successes out of $n$ trials in a binomial distribution, what is the probability $p$ of getting a success in each individual trial?
Presumably $p = s/n$, but what if $s = 0$ or $s = n$? Would the probability $p$ really be $0$ or $1$?
That seems far too certain if the sample size $n$ is very small, so is there some correction factor to account for small sample sizes in estimating $p$?