No need to be that exact. If I knew that:
Pixel Q is looking at a part of an object, which is P inches away from the camera.
My chosen maximum visibility in the fog is V inches.
Pixel Q without fog has color C.
The color of the fog is F.
Then I could calculate: set R=P/V; if R>1 then set R=1; set pixel Q to color (F * R) + (C * (1-R))