Why do some prey species actually stalk and follow cheetahs? I saw this on TV?

Yeah, what smurf! said. You'll also sometimes see this in birds - not so much the 'mobbing' behavior, where groups of small (prey) birds will har a large (predator) birds in an effort to drive it away, or at least make its location obvious, but rather flocks of birds in flight may sometimes follow a hunting Accipiter for at least a little while after it's missed its initial attack. By keeping tightly grouped, and behind the predator, they have a better chance of avoiding being eaten than if they don't where the predator is and are behaving normally.