What you are describing is not belief, but faith. Intuition is a quality of faith, not belief. Modern English interprets belief and faith as being the same thing, but they are not.
We interpret them in his way:
belief: Although in ancient times belief meant "trust in God," it is now merely "mental acceptance of something as true." Nowadays people believe many illogical, nonsensical, and absurd things. In fact, belief is related to belie, "to deceive by lies," from be- + lie (v.1) "to lie, tell lies."
That is why we prefer:
faith: from Greek Pistis. In Greek mythology, Pistis (Πίστις) was the personification of good faith, trust and reliability.
Pistis is based on experience and truth.
Study this lecture:
Belief and Faith.