Photographs of lightning taken with a streak camera show clearly that
a lightning stroke along one path is followed within a second or two
by several more, twenty or more in some cases. The technique is very
clever and very simple, a camera invented by C. V. Boys. It also
gives evidence for the direction of the stroke. There is a wonderful
book on this topic which, though somewhat out of date, is the best
reference I know to direct students to. It is "The Flight of Thunder-
bolts" by B. J. F. Schonland.
Now to answer the question: Once the ionized path is established by
the first flash in the stroke, the immediate charge being discharged
thereby, it takes a fraction of a second for charge to flow within
the thundercell to recharge the "capacitor" which was discharged.
When the potential difference between there and the ground again
reaches breakdown voltage, the previously established ion path is
still there as the path of least resistance, and that is where the
next stroke is most likely to go. Sometimes there can be seen small
variations in path from substroke to subtroke, but once the cloud is
fully discharged by internal electric currents it takes twenty
seconds or so to recharge by the mechanism driven by convective
updrafts in the cell.
The latest interesting related topics have to do with "sprites" and
some other name I always forget, colored light displays at the tops
of tall thundercells. Gamma rays are also seen to originate at these
places.
Another good place to look for information about atmospheric
electricity is Feynman's Volume II.