  The distribution of differential time delays \Delta t between images produced
by strong gravitational lensing contains information on the mass distributions
in the lensing objects as well as on cosmological parameters such as H_0. We
derive an explicit expression for the conditional probability distribution
function of time delays P(\Delta t|\theta), given an image separation between
multiple images \theta, and related statistics. We consider lensing halos
described by the singular isothermal sphere (SIS) approximation and by its
generalization as proposed by Navarro, Frenk, & White (NFW) which has a density
profile \rho \propto r^{-\alpha} in the innermost region. The time delay
distribution is very sensitive to these profiles; steeper inner slopes tend to
produce larger time delays. For example, if H_0=70 km/s/Mpc, a
\Lambda-dominated cosmology and a source redshift z_S=1.27 are assumed, lenses
with \theta=5'' produce a time delay of \Delta t[yr]=1.5^{+1.7}_{-0.9},
0.39^{+0.37}_{-0.22}, 0.15^{+0.11}_{-0.09}, and 0.071^{+0.054}_{-0.038} (50%
confidence interval), for SIS, generalized NFW with \alpha=1.5, \alpha=1.0, and
\alpha=0.5, respectively. At a fixed image separation, the time delay is
determined by the difference in the lensing potential between the position of
the two images, which typically occur at different impact parameters. Although
the values of \Delta t are proportional to the inverse of H_0, P(\Delta
t|\theta) is rather insensitive to all other cosmological model parameters,
source redshifts, magnification biases and so on. A knowledge of P(\Delta
t|\theta) will also be useful in designing the observing program of future
large scale synoptic variability surveys and for evaluating possible selection
biases operating against large splitting lens systems.
