Mathematical probability calculations are unlikely to assuage fears arising from arbitrary notions. Imagine, for example, that someone is convinced that an evil demon is under his bed. Even if we assume that a careful inspection has a 99% probability of uncovering this demon, an inspection with negative results would not prove mathematically that the fear was unfounded. In fact, if we suppose a 100% "prior probability" that the demon was real, then that probability will remain at 100%, no matter how many unsuccessful searches are conducted.