Pardon the semantic interruption here. Is "belief" defined only as knowing something without proof? What verb is more appropriate for this sample sentence?
"I believe that gravity exists, and I will fall if I lean too far over the edge."
However if I claim that I "know" there are fairies at the bottom of my garden most people will (correctly) point out that it is a non-verifiable statement and is a belief system. Belief and knowledge are not the same thing.