  We study the effect of site dilution in Kitaev's model. We derive an
analytical solution of the dynamical spin correlation functions for arbitrary
configurations of $Z_2$ fluxes. By incorporating this solution into classical
Monte Carlo scheme, we address how a site vacancy affects the experimental
observables, such as the static spin susceptibility and the spin lattice
relaxation rate, $1/T_1$. As a result, we found an enhancement of dynamical
magnetic response in the vicinity of vacancy, which leads to Friedel-like
oscillation in local $1/T_1$, in contrast to limited influences on the static
susceptibility. Furthermore, we found a sharp zero-energy peak in the magnetic
excitation spectrum, which is attributed to the Vison & Majorana zero mode
trapped near the site vacancy. This zero mode can be interpreted as
fractionalized spin hole into an Ising triplet with differentiated magnetic
axes, which leads to the characteristic temperature and field-orientational
dependence of $1/T_1$.
