How does the height of a cloud influence the probability of precipitation?

The higher the cloud is, less chance for precipitation to fall because the clouds are way up in the air, so it wouldn't be as thick as lower cloud would be. The lower the cloud is the better chance that you would see precipitation because you can see the thickness, you could like cloud wants to give off all its water in the form of precipitation, and you could see that it is about to rain. In clouds that are high, you would see them there for a long time that you wouldn't see i droplet of precipitation. 

Is there a picture of the diagram?