Example of Markov process not having transition density function

Question

I try to construct a Markov process that does not have a transition density function.

Let $m$ be a positive Radon measure and $E$ be a locally compact separable metric space (state space). I am considering a $m$symmetric Markov process $\{X_t\}$ such that $m(B)=0$ and $P_x(X_t\in B)>0$ for some Borel set $B$ and some $x\in E$.

Someday knows such an example?