Laplace's Rule of Succession

Given a repeated set of $n$ independent experiments $X_i$ with $s$ successes ($X_i=1$), what is the probability of the $n+1$ experiment being a success:

$$P(X_{n+1}=1|\sum_{i=1}^{n} {X_i}=s) = \frac{s+1}{n+2}$$

This is known as Laplace’s Rule of Succession.