  The gravitational-wave GW170817 is associated to the inspiral phase of a
binary neutron star coalescence event. The LIGO-Virgo detectors sensitivity at
high frequencies was not sufficient to detect the signal corresponding to the
merger and post-merger phases. Hence, the question whether the merger outcome
was a prompt black hole formation or not must be answered using either the
pre-merger gravitational wave signal or electromagnetic counterparts. In this
work we present two methods to infer the probability of prompt black hole
formation, using the analysis of the inspiral gravitational-wave signal. Both
methods combine the posterior distribution from the gravitational-wave data
analysis with numerical relativity results. One method relies on the use of
phenomenological models for the equation of state and on the estimate of the
collapse threshold mass. The other is based on the estimate of the tidal
polarizability parameter $\tilde{\Lambda}$ that is correlated in an
equation-of-state agnostic way with the prompt BH formation. We analyze
GW170817 data and find that the two methods consistently predict a probability
of ~ 50-70% for prompt black-hole formation, which however may significantly
decrease below 10% if the maximum mass constraint from PSR J0348+0432 or PSR
J0740+6620 is imposed.
