Let $\{X_t,t \geq0\}$ with state space $[0,1]$ be a regular diffusion process. Assume that $0$ and $1$ are exit boundaries.
Then, $\{X^*_t,t\geq0\}$ is prescribed to be the process confined to the sample paths involving ultimate absorption at 1.
Which formal argument(s) can be applied to confirm that $\{X^*_t, t\geq 0\}$ is a Markov process?