  The combination of the first-year Wilkinson Microwave Anisotropy Probe (WMAP)
data with other finer scale cosmic microwave background (CMB) experiments (CBI
and ACBAR) and two structure formation measurements (2dFGRS and Lyman $\alpha$
forest) suggest a $\Lambda$CDM cosmological model with a running spectral power
index of primordial density fluctuations. Motivated by this new result on the
index of primordial power spectrum, we present the first study on the predicted
lensing probabilities of image separation in a spatially flat $\Lambda$CDM
model with a running spectral index (RSI-$\Lambda$CDM model). It is shown that
the RSI-$\Lambda$CDM model suppress the predicted lensing probabilities on
small splitting angles of less than about 4$^{''}$ compared with that of
standard power-law $\Lambda$CDM (PL-$\Lambda$CDM) model.
