Incredulity is the state of not believing. I greeted the stranger's story about needing bus fare with incredulity. "I just don't believe you," I said. "The bit about your diabetic cat was a little over the top."
In Latin, credere means "to believe." You'll see it at the roots of creed "statement of belief," credible "believable," credulous "a person who readily believes," and incredulous "a person who doesn't."