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 $\mathrm{H}(x’,\tau’)$. When the height $\mathrm{H}(x’,\tau’)$ 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 three lower order

error terms can be expressed as the derivatives of of the GUE Tracy-Widom

distribution. These KPZ-type limiting behaviors are different from the

Gaussian-type ones obtained in [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 prove, with the step

initial condition, 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.