  We study the probability that three GRBs (980425, 030329, 031203) are found
within z=0.17, given the luminosity functions consistent with the log N-log S
relationship for classical cosmological bursts (i.e., those observed by BATSE).
We show that, in order for the probability of these three low-z events to be
non-negligible (thus making it more likely that they belong to the same class
of the classical cosmological bursts), the bursts' luminosity function must be
a broken powerlaw. By reasoning in analogy with beamed AGNs, we show that
observations are consistent with the expectations if GRB 980425 and GRB 031203
are indeed normal bursts seen sideways. Within this model, no bright burst
within z=0.17 should be observed by a HETE--like instrument within the next
\sim 20 yr.
