 $$P_u \left( \tau_\varepsilon < e^{\frac{\Delta - \delta}{\varepsilon^0}} \right) \leq P_u \left( \tau_\varepsilon(B_c) > \tau_{\mathcal{K},\frac{c}{0}} \right) + P_u \left( \tau_\varepsilon \leq \tau_{\mathcal{K},\frac{c}{0}}\right) + \sup_{v \in B_c} P_v \left( \tau_\varepsilon < e^{\frac{\Delta - \delta}{\varepsilon^0}} \right)$$ and $$P_u \left( \tau_\varepsilon > e^{\frac{\Delta + \delta}{\varepsilon^0}} \right) \leq P_u \left( \tau_\varepsilon(B_c) > \tau_{\mathcal{K},\frac{c}{0}} \right) + \sup_{v \in B_c} P_v \left( \tau_\varepsilon > e^{\frac{\Delta + \frac{\delta}{0}}{\varepsilon^0}} \right)