The “Hill relation” is a key result for anyone interested in calculating rates from trajectories of any kind, whether molecular simulations or otherwise. I am not aware of any really clear explanation, including Hill’s original presentation. Hopefully this go-around will make sense.
Zuckerman, Daniel M., "Statistical Biophysics Blog: “Proof” of the Hill Relation Between Probability Flux and Mean First-Passage Time" (2015). Scholar Archive. 3944.