I know the dictionary definitions and explicitly addressed the case that you are sticking to them. But the words have connotations beyond the dictionary definitions.
If you do not rule out the possibility (p), then you believe (b) that a divine entity exist (1), even if you do not know how to prove the existence of what you perceive:
1 ∈ p ∉ 0
Therefore you are a theist:
p ∈ b ∴ 1 ∃ b
I don't understand your argument or its notation. "Believing that X could be true" is not the same as "Believing that X is true and not knowing how to prove it".
Which goes back to Graham's point - you seem to be wanting me to "pick a side" instead of treating it like any other statement that one can be uncertain about.