One aspect of this, though, is the butterfly effect is an aspect of certain *deterministic* systems. In these system, the result is *determined* once the initial conditions are set. But, if the initial conditions are slightly different, the system evolves in a very different way.
And yes, one of the difficulties is that chaotic systems (those deterministic systems with sensitive dependence on initial conditions) cannot be precisely predicted and thereby *look* like probabilistic systems, even though they are not.
So, yes, in a *classical* system, in which the basic physical laws are deterministic, the physics *does* determine when the rabbit will decide to move. And that was determined by the initial conditions billions of years ago. The fact that if the initial conditions were slightly different there may not have been a rabbit at all does not negate the deterministic aspect of the system.
Now, we know that the real world is NOT deterministic in this sense. Quantum mechanics has an inherent and unavoidable probabilistic nature. One question that has not been sufficiently investigated, I think, is what happens to quantum systems that would be chaotic in classical physics.
But I'm not sure that quantum mechanics saves free will. If anything, it seems to make the problems even more significant. Instead of our choices being determined by initial conditions billions of years ago, they are determined by random processes right now.
Nobody disagrees with the fact that we all have at least an *illusion* of free will. The question is whether that illusion actually matches reality in some way and, if so, the specifics of that matching.