Equidistribution of polynomial roots modulo primes with root-count normalization

Let $f\be\in\mathbf{Z}[X]$ be a monic irreducible polynomial of degree at least $2$. Let $\Pi_f(x)$ denote the set of primes $p\leqslant x$ for which $f$ has at least one root modulo $p$, and let $\Delta_p$ be the uniform probability measure on the roots of $f$ modulo $p$. Equidistribution conjecture. The measures

$$\frac{1}{|\Pi_f(x)|}\sum_{\substack{p\leqslant x\p\in\mathcal{Q}}}\Delta_p$$

converge to the uniform measure as $x\to+\infty$. This is the qualitative equidistribution conjecture corresponding to the paper's theorem; the source presents it as a potential conjecture and gives no resolution.