KURSCHAK 2017 Problem 1

Let $ABC$ be a triangle. Choose points $A'$ , $B'$ and $C'$ independently on side segments $BC$ , $CA$ and $AB$ respectively with a uniform distribution. For a point $Z$ in the plane, let $p(Z)$ denote the probability that $Z$ is contained in the triangle enclosed by lines $AA'$ , $BB'$ and $CC'$ . For which interior point $Z$ in triangle $ABC$ is $p(Z)$ maximised?