The gravitational wave GW170817 is associated with 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 postmerger phases. Hence, the question whether the merger outcome was a prompt black-hole formation or not must be answered using either the premerger 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 Λ ∼ that is correlated in an equation-of-state agnostic way with the prompt black-hole 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.