Let $(X_t)_{t\ge0}$ be a Lévy process, $\tau_0:=0$ and $$\tau_n:=\{t>\tau_{n-1}:\Delta X_t\in B\}\;\;\;\text{for }n\in\mathbb N$$ for some measurable set $B$ with $0\not\in B$.
How can we show that $$\ln\operatorname P[\tau_1>1]=-\lambda(B),$$ where $$\lambda(B):=\operatorname E[\pi_1(B)]$$ and $$\pi_t(B):=\sum_{n\in\mathbb N}1_{[0,\:t]}(\tau_n)?$$