Let $E$ be an infinite countable subset of $\mathbb{R}$. Let $(\Omega, \mathscr{A}, P)$ be a probability space. Let $X$ be a random variable defined on $(\Omega, \mathscr{A}, P)$ and taking values in $E$. We call the law of the variable $X$ and we denote $\mu_X$ the application where $\{X \in A\} = \{\omega \in \Omega \text{ such that } X(\omega) \in A\}$. Verify that $\mu_X$ is a probability on $E$.