I'm working on a spatial project. I need to calculate the probability of a point being the closest to another. Say I'm given four points $y$, $x_1$,$x_2$ and $x_3$ in 2D plane, and let $Y'=y+Z$, where $Z$ is a bivariate normal with known mean and covariance. I want to know the probability that $x_1$ out of the three $x$'s is closest to $Y'$. How should I proceed? Thank you very much!