Hurricane has 70% accuracy without rain, and a 30% chance to confuse the opponent if it hits. Heat Wave has a 90% chance to hit and a 10% chance to burn if it hits. While confused, a Pokemon has a 30% chance to hit itself per turn.
So that's:
7/10 * 3/10 * 9/10 * 1/10 * 3/10 * 3/10 = 1,701/1,000,000, or approximately 1/588 or a 0.1701% chance.