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.

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