  We study the Horizon Wave Function (HWF) description of a generalized
uncertainty principle (GUP) black hole in the presence of two natural cutoffs
as a minimal length and a maximal momentum. This is motivated by a metric which
allows the existence of sub-Planckian black holes, where the black hole mass
$m$ is replaced by
$M=m\Big(1+\frac{\beta^{2}}{2}\frac{M_{pl}^{2}}{m^{2}}-\beta\frac{M_{pl}}{m}\Big)$.
Considering a wave-packet with a Gaussian profile, we evaluate the HWF and the
probability that the source might be a (quantum) black hole. By decreasing the
free parameter the general form of probability distribution,
${\mathcal{P}}_{BH}$, is preserved , but this resulted in reducing the
probability for the particle to be a black hole accordingly. The probability
for the particle to be a black hole grows when the mass is increasing slowly
for larger positive $\beta$, and for a minimum mass value it reaches to $0$. In
effect, for larger $\beta$ the magnitude of $M$ and $r_{H}$ increases, matching
with our intuition that either the particle ought to be more localized or more
massive to be a black hole. The scenario undergoes a change for some values of
$\beta$ significantly, where there is a minimum in ${\mathcal{P}}_{BH}$ , so
this expresses that every particle can have some probability of decaying to a
black hole. In addition, for sufficiently large $\beta$ we find that every
particle could be fundamentally a quantum black hole.
