I think you shouldn't think too hard about these problems. Literally ANYTIME you see a K (Ksp, Ka, Kb, Kp) you can think about the ICE table. It tells you the initial pressures & total pressure at equilibrium, from there you just have to identify that the equilibruim values are what they're looking for. You HAVE to get these values to plug in for the equation for Kp. Hope this helps.