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(1+ β2/2m2 plm2 −βmplm ). 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, PBH, 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 β, and for a minimum mass value it reaches to 0. In effect, for larger β the magnitude of M and rH 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 β significantly, where there is a minimum in PBH, so this expresses that every particle can have some probability of decaying to a black hole. In addition, for sufficiently large β, we find that every particle could be fundamentally a quantum black hole.
