The really difficult to grasp word here is belief. It can cover so many things.
I firmly believe that a clear daytime sky on earth is always blue. There's no intuition involved, I've never seen differently. Nor have I heard a credible report of anything else. I can't prove it to anybody else though, not if they refuse to come out from under their blankets.
Similarly, I believe in God but not religion. Its clear to me that religion is fiction, invented by humans for a variety of reasons. Some reasons are better than others, but still. As a result, I don't "believe". This despite believing in a great many things, including God. There's no intuition involved here either. It's as evidence based as my beliefs about the sky.
Tom