The calculated sensitivity will never change if you have the same DPI in both Windows and the game. If you just change DPI in the first box, it will be copied to the second box unless you have entered a value in it too.
So when you change from say 400 to 800, you are doubling your "sensitivity" in Windows, making the distance half. So to match this the same thing has to happen in the game, you should have half the distance. But since you doubled your DPI, the distance is already half and the sensitivity stays the same.