  Using Monte-Carlo simulations, we determine the scaling form for the
probability distribution of the shortest path, $\ell$, between two lines in a
3-dimensional percolation system at criticality; the two lines can have
arbitrary positions, orientations and lengths. We find that the probability
distributions can exhibit up to four distinct power law regimes (separated by
cross-over regimes) with exponents depending on the relative orientations of
the lines. We explain this rich fractal behavior with scaling arguments.
