  In the setting of non-reversible Markov chains on finite or countable state
space, exact results on the distribution of the first hitting time to a given
set $G$ are obtained. A new notion of "strong metastability time" is introduced
to describe the local relaxation time. This time is defined via a
generalization of the strong stationary time to a "conditionally strong
quasi-stationary time"(CSQST). Rarity of the target set $G$ is not required and
the initial distribution can be completely general. The results clarify the the
role played by the initial distribution on the exponential law; they are used
to give a general notion of metastability and to discuss the relation between
the exponential distribution of the first hitting time and metastability.
