We recently improved the famous result of Parikh and Wilczek, who found a probability of emission of Hawking radiation that is compatible with a non-strictly thermal spectrum, showing that such a probability of emission is really associated with two non-strictly thermal distributions for bosons and fermions. Here, we finalize the model by finding the correct value of the pre-factor of the Parikh and Wilczek probability of emission. In fact, that expression has a ∼ sign instead of the equality. In general, in this kind of leading order tunneling calculation, the exponent indeed arises from the classical action, and the pre-factor is an order of Planck constant correction. But in the case of emissions of Hawking quanta, the variation of the Bekenstein–Hawking entropy is of the order of 1 for an emitted particle with energy of the order of the Hawking temperature. As a consequence, the exponent in the Parikh and Wilczek probability of emission is of the order of unity and one asks, what is the real significance of that scaling if the pre-factor is unknown? Here we solve the problem assuming the unitarity of the black hole (BH) quantum evaporation and considering the natural correspondence between Hawking radiation and quasi-normal modes (QNMs) of excited BHs, in a ‘Bohr-like model’ that we recently discussed in a series of papers. In those papers, QNMs are interpreted as natural BH quantum levels (the ‘electron states’ in the ‘Bohr-like model’). Here we find the intriguing result that, although in general it is well approximated by 1, the pre-factor of the Parikh and Wilczek probability of emission depends on the BH quantum level We also write down an elegant expression of the probability of emission in terms of the BH quantum levels.