continuous time markov process - first passage time

Question

Let $(X_t)_{t\ge0}$ is a continuous time-homogeneous Markov diffusion process such that $X_0=y$. Let $$p(x,t|y)=d\Pr(X_t\le x|X_0=y)/dx$$ be the respective transition probability density. Let $$T_{y,a}=\inf\{t\ge0\colon X_t\ge a\}$$ Would it be correct to claim that $$ \Pr(T_{y,a}>\tau)=\int_{-\infty}^a p(x,\tau|y)\,dx, $$ or what's the connection between $\Pr(T_{y,a}>\tau)$ and $p(x,\tau|y)$?