We report the electronic and superconducting properties in the Pr-based filled-skutterudite superconductor PrRu$_4$Sb$_{12}$ with $T_c = 1.3$ K via the measurements of nuclear-quadrupole-resonance (NQR) frequency $ u_Q$ and nuclear-spin-lattice-relaxation time $T_1$ of Sb nuclei. The temperature dependence of $ u_Q$ has revealed the energy scheme of Pr$^{3+}$ crystal electric field (CEF) that is consistent with an energy separation $Delta_{CEF}sim 70$K between the ground state and the first-excited state. In the normal state, the Korringa relation of $(1/T_1T)_{Pr}$=const. is valid, with [$(1/T_{1}T$)$_{Pr}$/$(1/T_{1}T$)$_{La}$]$^{1/2}$ $sim$ 1.44 where $(1/T_1T)_{La}$ is for LaRu$_4$Sb$_{12}$. These results are understood in terms of a conventional Fermi liquid picture in which the Pr-$4f^2$ state derives neither magnetic nor quadrupolar degrees of freedom at low temperatures. In the superconducting state, $1/T_1$ shows a distinct coherence peak just below $T_c$, followed by an exponential decrease with a value of 2$Delta/k_{B}T_{c}$ = 3.1. These results demonstrate that PrRu$_4$Sb$_{12}$ is a typical weak-coupling s-wave superconductor, in strong contrast with the heavy-fermion superconductor PrOs$_4$Sb$_{12}$ that is in an unconventional strong coupling regime. The present study on PrRu$_4$Sb$_{12}$ highlights that the Pr-$4f^2$derived non-magnetic doublet plays a key role in the unconventional electronic and superconducting properties in PrOs$_4$Sb$_{12}$.
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