The interval-valued hesitant fuzzy probability theory is investigated. The concepts of typical interval-valued hesitant fuzzy event and its probability have been introduced. The basic properties and Borel-Cantelli Lemma of classical probability are generalized to that of the probability of typical interval-valued hesitant fuzzy event. The continuity of the probability of interval-valued hesitant fuzzy event and ordering property for interval-valued hesitant fuzzy probability have been discussed.