  We show that holographic dark energy could explain why the current dark
energy density is so small, if there was an inflation with a sufficient
expansion in the early universe. It is also suggested that an inflation with
the number of e-folds $N\simeq 65$ may solve the cosmic coincidence problem in
this context. Assuming the inflation and the power-law acceleration phase today
we obtain approximate formulas for the event horizon size of the universe and
dark energy density as functions of time. A simple numerical study exploiting
the formula well reproduces the observed evolution of dark energy. This
nontrivial match between the theory and the observational data supports both
inflation and holographic dark energy models.
