  The action for a relativistic free particle of mass $m$ receives a
contribution $-mds$ from a path segment of infinitesimal length $ds$. Using
this action in a path integral, one can obtain the Feynman propagator for a
spinless particle of mass $m$. If one of the effects of quantizing gravity is
to introduce a minimum length scale $L_P$ in the spacetime, then one would
expect the segments of paths with lengths less than $L_P$ to be suppressed in
the path integral. Assuming that the path integral amplitude is invariant under
the `duality' transformation $ds\to L_P^2/ds$, one can calculate the modified
Feynman propagator. I show that this propagator is the same as the one obtained
by assuming that: quantum effects of gravity leads to modification of the
spacetime interval $(x-y)^2$ to $(x-y)^2+L_P^2$. This equivalence suggests a
deep relationship between introducing a `zero-point-length' to the spacetime
and postulating invariance of path integral amplitudes under duality
transformations.
