Strictly speaking this is just a special case of what should be addressed by How do I know which article to use?, but I'm afraid no answer there seems to directly address the specific current case.
There's no context to have an opinion on example #2 above, but #1 could quite reasonably use the, a, or the "zero article". I'm inclined to think that the may (very slightly) elevate the status of belief. If you want to be "literal", it implies the only [significant] belief (it's been "particularized", with the implication that we all know which belief we're talking about). So an Anglophone Muslim might (again, slightly) prefer that version.
Correspondingly therefore, one might suppose that using the indefinite article a slightly downgrades the status of the belief (since there's an implication that it's just one of many beliefs). So feasibly an atheist might prefer that version.
To round it off, I could say that using the zero article (as Collins did it their citation) steers a more neutral middle path. But to be honest, these three "distinctions" are becoming progressively more tenuous. It's far easier (and probably accurate) to just say they're equivalent/interchangeable.
The actual word belief isn't inherently countable or uncountable. Depending on context (surrounding syntax and intended meaning) it can be either.