I would define belief as the involuntary judgment of an idea as being true based on certain thoughts or evidence that seem to point to it being true but without constituting absolute proof of its truthfulness. For when there is absolute proof it is no longer a belief but knowledge.
Belief is basically like gambling. Take professional horse-racing gamblers as an example. They judge the odds of a particular horse winning based its track record, the jockey, it's age, past injuries, etc. None of these factors (when in the favor of the horse) allow them to have absolute knowledge that the horse will win. But it does serve to sway the mind to think that the horse most probably will win and so they bet on the horse. Well it's similar with belief. How easily the mind of the believer is convinced differs from person to person depending on their critical thinking skills and gullibility.
Doubt or lack of certainty is an essential aspect of belief. The difference between belief and knowledge is lack of certainty. If there is no uncertainty then it is not belief but knowledge. If the lack of uncertainty is not due to sound absolute proof then its not knowledge but delusion.
Anyone who says they know God exists is someone I see as being either dishonest or delusional. Even the bible does not require worshipers to know that God exists. Hebrews 11:6 says that a person has to believe that God exists to be favorably heard by him.