For mountain ranges that are subjected to prevailing winds, why is the climate drier on the leeward (downwind) side?

For the mountain ranges that are subjected to prevailing winds, the climate is dryer on the leeward side because the clouds with the rains either do not pass, or pass but are mostly dried out. This is because the other side of the mountain range stops the clouds and the rain falls predominantly on that side, so the clouds either do not pass at all on the leeward side, or if some of them manage to pass, they have very little moisture left so the rain is obscure, thus the leeward sides are usually dry.