  We consider the Kardar-Parisi-Zhang (KPZ) fixed point $\mathrm{H}(x,\tau)$
with the step initial condition and investigate the distribution of
$\mathrm{H}(x,\tau)$ conditioned on a large height at an earlier space-time
point $\mathrm{H}(x',\tau')$. As $\mathrm{H}(x',\tau')$ tends to infinity, we
prove that the conditional one-point distribution of $\mathrm{H}(x,\tau)$ in
the regime $\tau>\tau'$ converges to the Gaussian Unitary Ensemble (GUE)
Tracy-Widom distribution and the next two lower-order error terms can be
expressed as derivatives of the GUE Tracy-Widom distribution, which is a
conceptual analogue to the Edgeworth expansion in the central limit theorem.
These KPZ-type limiting behaviors are different from the Gaussian-type ones
obtained in \cite{Liu-Wang22} where they study the finite-dimensional
distribution of $\mathrm{H}(x,\tau)$ conditioned on a large height at a later
space-time point $\mathrm{H}(x',\tau')$. They show, with the step initial
condition, that the conditional random field $\mathrm{H}(x,\tau)$ in the regime
$\tau<\tau'$ converges to the minimum of two independent Brownian bridges
modified by linear drifts as $\mathrm{H}(x',\tau')$ goes to infinity. The two
results stated above provide the phase diagram of the asymptotic behaviors of a
conditional law of KPZ fixed point in the regimes $\tau>\tau'$ and $\tau<\tau'$
when $\mathrm{H}(x',\tau')$ goes to infinity.
