The binding of a drug molecule to a protein is a complex biophysical process in which water plays a critical role. To understand the fundamental mechanisms of such a process, we have developed a new and efficient approach that combines our level-set variational implicit-solvent model with the string method for transition paths, and have studied the pathways of drying transition in a model ligand-receptor system. We further carry out Brownian dynamics simulations as well as Fokker-Planck equation modeling with our efficiently calculated potential of mean force to describe the important effect of the solvent fluctuations to the kinetics of binding and unbinding. Our work demonstrates that rigorous mathematical development can contribute to the challenging scientific study of molecular recognition, and drug design.