  Recently, two of us argued that the probability that an FK cluster in the
Q-state Potts model connects three given points is related to the time-like
Liouville three-point correlation function. Moreover, they predicted that the
FK three-point connectivity has a prefactor which unveils the effects of a
discrete symmetry, reminiscent of the S_Q permutation symmetry of the Q=2,3,4
Potts model. Their theoretical prediction has been checked for the case of
percolation, corresponding to Q=1. We revisit the derivation of the time-like
Liouville correlator given by Al. Zamolodchikov and show that this is the the
only consistent analytic continuation of the minimal model structure constants.
We then present strong numerical tests of the relation between the time-like
Liouville correlator and percolative properties of the FK clusters for real
values of Q.
