Inertia of Kraus matrices

For positive real numbers $r$, $p\_0$, and $p\_1 < \cdots p\_n,$ let $K\_r$ be the $n \times n$ Kraus matrix whose $(i,j)$ entry is equal to $$ \frac{1}{p\_i - p\_j} \Bigl( \frac{p\_i^r p\_0^r}{p\_i -p\_0} \frac{p\_j^r p\_0^r}{p\_j \Bigr). We determine inertia of this matrix.