  We explore the thermodynamics and the underlying kinetics of the van der
Waals type phase transition of Reissner-Nordstr\"{o}m anti-de Sitter (RNAdS)
black holes based on the free energy landscape. We show that the thermodynamic
stabilities of the three branches of the RNAdS black holes are determined by
the underlying free energy landscape topography. We suggest that the large
(small) RNAdS black hole can have the probability to switch to the small
(large) black hole due to the thermal fluctuation. Such a state switching
process under the thermal fluctuation is taken as a stochastic process and the
associated kinetics can be described by the probabilistic Fokker-Planck
equation. We obtained the time dependent solutions for the probabilistic
evolution by numerically solving Fokker-Planck equation with the reflecting
boundary conditions. We also investigated the first passage process which
describes how fast a system undergoes a stochastic process for the first time.
The distributions of the first passage time switching from small (large) to
large (small) black hole and the corresponding mean first passage time as well
as its fluctuations at different temperatures are studied in detail. We
conclude that the mean first passage time and its fluctuations are related to
the free energy landscape topography through barrier heights and temperatures.
