We report on the measurement of ratios of branching ratio of decays $B \to K\mu\mu$ and $B \to Kee$, dubbed as $R_{K}$, using a data sample of 711 fb$^{-1}$ at $\Upsilon(4S)$ resonance recorded by the Belle detector. In addition, we have measured the CP-averaged isospin asymmetry and differential branching ratio of these decays. These observables are calculated in the bins of di-lepton invariant mass squared, $q^2$. We have also searched for lepton-flavor-violating $B \to K\mu^{\pm}e^{\pm}$ decays. The upper limits on the branching ratio are ${\cal B}(10^{-8})$. We improve the existing upper limit on $B^0 \to K_{S}^{0}\mu^{\pm}e^{\mp}$ an order of magnitude, ${\cal B}(B^0 \to K_{S}^{0}\mu^{\pm}e^{\mp})< 3.8 \times 10^{-8}$ at $90\%$ confidence level.