The problem:

Let G = (V, E) be a directed graph on n >= 3 vertices with m edges. The vertex set V includes three
special vertices a, v, and b. Find a simple path from a to b via v if it exists. (A simple path is a path without repeated vertices.)

I believe this problem should/can be solved with a Max Flow algorithm but I am not sure how. It reminds me of a Max Flow algorithm with multiple sources where the edges have capacity 1. Anyone know how the problem can be reduced to Maximum flow algorithm?

If I set vertex b as sink I can not be sure it will include v. If I set v as sink how do I continue when v is reached?