Let $p$ be a prime. We select $x_1,x_2,\cdots,x_n\in\mathbb{Z}_p$ randomly and uniformly. Let $V$ denote the Vandermonde determinant $$ V_n= \left\vert\begin{matrix} 1 & x_1 & x_1^2 & \cdots & x_1^{n-2} & x_1^{n-1} \\ 1 & x_2 & x_2^2 & \cdots & x_2^{n-2} & x_2^{n-1} \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 1 & x_n & x_n^2 & \cdots & x_n^{n-2} & x_n^{n-1} \end{matrix}\right\vert mod p. $$ of the elments of $\mathbb{Z}/p\mathbb{Z}$.
What is the probability distribution of the vandermonde determinant over a finite field $\mathbb{Z}_p$?