We explore possibility of computing solutions of a certain type of infinitely dimensional Hamilton-Jacobi equations in probability space that arises in the theory of mean field games. Numerical solution to such HJ-PDE was difficult owing to the high dimension of the PDE after discretization of a function space. We propose to utilize a Hopf formula coming from an optimal control approach. The resulting formula is an optimization problem involving a d dimensional HJ-PDE constraint, i.e. the mean field equations, which can be computed using a standard finite difference scheme. In particular, our method will provide us one possible way to compute proximal maps of Wasserstein metrics. They may be of importance in computing optimization problems involving Wasserstein metrics. Our techniques may have applications in optimal transport, mean field games and optimal control in the space of probability densities.