  From the viewpoint of holography, the phase structure of a 5-dimensional
Reissner-Nordstr\"{o}m-AdS black hole is probed by the two point correlation
function, Wilson loop, and entanglement entropy. As the case of thermal
entropy, we find for all the probes, the black hole undergos a Hawking-Page
phase transition, a first order phase transition and a second order phase
transition successively before it reaches to a stable phase. In addition, for
these probes, we find the equal area law for the first order phase transition
is valid always and the critical exponent of the heat capacity for the second
order phase transition coincides with that of the mean field theory regardless
of the size of the boundary region.
