Madness, followed by some of the clergy desperately embracing a religion - ANY religion, even the evil ones - that will give them that divine connection they crave so much. The others, embittered by the loss of their power, go full-on athiest and begin denouncing all the gods in public. Maybe a very, very few, fueled by natural faith, get to keep their powers, but this is in the absolute minority (i.e., one or two of the PCs, and possibly one other NPC they run across in their travels).