I've always found belief a bit difficult; people tend to assume that I have rather strong beliefs, but I don't experience them in that way. As far as knowledge goes I'm a consumer, and sometimes a distributor, not a producer; most of what I believe to be true lies far beyond my capacity for proof, and I try to moderate the timbre of my belief accordingly. I know that almost all my beliefs are based on faith in people, and processes, and institutions, and their various capacities for correcting themselves when in error.
I think the same is true for most of us; those who can prove their beliefs in their field of expertise are still reliant on faith in others when it comes to other fields. To acknowledge this at all times is not possible—it would make every utterance tentative, encrust every concept with ceteris paribus clauses. But when faced with a question like this, the role of our faith in people and in social institutions has to be acknowledged. And it does no harm to acknowledge it now and then even when not faced with such a question, in order to reinforce the need to keep people, institutions and the processes of knowledge production held in helpful scrutiny.
Which I suppose means that, for me, the real question is what do I believe that I don't think anyone can prove. In answer I'd put forward the belief that there is a future much better, in terms of reduced human suffering and increased human potential, than the present, and that one part of what makes it better is a greater, subtler knowledge of the world at large.
If I can't prove this, why do I believe it? Because it's better than believing the alternative. Because it provides a context for social and political action that would otherwise be futile; in this, it is an exhortatory belief. It is also, in part, a self-serving one, in that it suggests that by trying to clarify and disseminate knowledge (a description that makes me sound like the chef at a soup kitchen) I'm doing something that helps the better future, if only a bit.
Besides the question of why, though, there's the question of how. And there the answer is "with difficulty". It is not an easy thing for me to make myself believe. But it is what I want to believe, and on my best days I do.