Problem 6 (2019 AMC 8)

There are $81$ grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point $P$ is the center of the square. Given that point $Q$ is randomly chosen from among the other $80$ points, what is the probability that line $PQ$ is a line of symmetry for the square? [See figure in original PDF]