If someone has an experience that is proof....how do you prove they do not?

That is true.

Belief requires no factual support. In many cases it even requires denials of facts that contradict the belief (where faith crosses over into willful ignorance).

Knowing on the other hand has a basis in provable facts.

Believing = opinion = hypothesis

And many confuse lack of belief for belief against.

Interesting point... so, I believe a country called Ireland exists because I have seen pictures and know people who have been there, so can I know it actually does? In my mind, yes, but not everyone agrees. Then the conversation usually devolves into some form of solipsism, which to me ignores a lot of hard evidence.

Maybe "belief" should be defined as claiming knowledge of something without adequate evidence; and perhaps also defined as an opinion.

That sound about right?