9. Given the inequality $\frac{x-5}{x+1}<0$ with the solution set $M$. If $x_{0} \in M$, then the probability that $\log _{2}\left(x_{0}+1\right)<1$ is ( ).
(A) $\frac{1}{4}$
(B) $\frac{1}{3}$
(C) $\frac{1}{5}$
(D) $\frac{2}{5}$
9. B.

From the problem, we know that $M=\{x \mid-1<x<5\}$.
And the solution set of $\log _{2}\left(x_{0}+1\right)<1$ is
$$
\{x \mid-1<x<1\} \text {, }
$$

Therefore, the required probability is $\frac{1}{3}$.