  The statistics of gravitational lensing can provide us with a very powerful
probe of the mass distribution of matter in the universe. By comparing
predicted strong lensing probabilities with observations, we can test the mass
distribution of dark matter halos, in particular, the inner density slope. In
this letter, unlike previous work that directly models the density profiles of
dark matter halos semi-analytically, we generalize the density profiles of dark
matter halos from high-resolution N-body simulations by means of generalized
Navarro-Frenk-White (GNFW) models of three populations with slopes, $\alpha$,
of about -1.5, -1.3 and -1.1 for galaxies, groups and clusters, respectively.
This approach is an alternative and independent way to examine the slopes of
mass density profiles of halos. We present calculations of lensing
probabilities using these GNFW profiles for three populations in various
spatially flat cosmological models with a cosmological constant $\Lambda$. It
is shown that the compound model of density profiles does not match well with
the observed lensing probabilities derived from the Jodrell-Bank VLA
Astrometric Survey data in combination with the Cosmic Lens All-Sky Survey
data. Together with the previous work on lensing probability, our results
suggest that a singular isothermal sphere mass model of less than about
$10^{13}h^{-1}M_{\sun}$ can predict strong lensing probabilities that are
consistent with observations of small splitting angles.
