We report a novel prediction from single-field inflation that even a tiny
step in the inflaton potential can change our perception of primordial
non-Gaussianities of the curvature perturbation. Our analysis focuses on the
tail of probability distribution generated by an upward step transition between
two stages of slow-roll evolution. The nontrivial background dynamics with
off-attractor behavior is identified. By using a non-perturbative $\delta N$
analysis, we explicitly show that a highly non-Gaussian tail can be generated
by a tiny upward step, even when the conventional nonlinearity parameters
$f_{NL}$, $g_{NL}$, etc. remain small. With this example, we demonstrate for
the first time the sensitive dependence of non-perturbative effects on the tail
of probability distribution. Our scenario has an inconceivable application to
primordial black holes by either significantly boosting their abundance or
completely forbidding their appearance.
