Hello! I've been using this kit everyday in order to go kill Court Warlock. Usually I do not need more than 5 times to succeed and there is no cooldown in between your attempts.
So assuming 5 times is a bad streak, I'd say chances should be in somewhere between 30 and 50%, but ir really shouldn't matter since you do not have to wait in order to attempt again.
Notice, though, that this shortcut is one-way only and you cannot go back through the same method