Let $x \in \mathbb{R}$ such that $x > 1$. Show that we define the probability distribution of a random variable $X$ taking values in $\mathbb{N}^{*}$ by setting $$\forall n \in \mathbb{N}^{*}, \quad \mathbb{P}(X = n) = \frac{1}{\zeta(x) n^{x}}$$
Let $x \in \mathbb{R}$ such that $x > 1$. Show that we define the probability distribution of a random variable $X$ taking values in $\mathbb{N}^{*}$ by setting
$$\forall n \in \mathbb{N}^{*}, \quad \mathbb{P}(X = n) = \frac{1}{\zeta(x) n^{x}}$$