  We investigate the dynamics of a generalized survival probability $S(t,R)$
defined with respect to an arbitrary reference level $R$ (rather than the
average) in equilibrium step fluctuations. The exponential decay at large time
scales of the generalized survival probability is numerically analyzed.
$S(t,R)$ is shown to exhibit simple scaling behavior as a function of
system-size $L$, sampling time $\delta t$, and the reference level $R$. The
generalized survival time scale, $\tau_s(R)$, associated with $S(t,R)$ is shown
to decay exponentially as a function of $R$.
