It only reduces the odds to such a tiny number if your password is in the list (otherwise, guessing the remaining 136 bits of the hash is infeasible). If that's

It only reduces the odds to such a tiny number if your password is in the list (otherwise, guessing the remaining 136 bits of the hash is infeasible). If that's the case, however, sending a part of the hash to the server is still the best idea, because you want to know that the password needs to be changed immediately. At this point, the 72^8 estimate no longer matters, both because the full list of HIBP passwords is much smaller than that and because you don't know if other information (such as the corresponding username) was leaked along with the password.