Density matrix approach has been employed to analyze the pump-probe spectroscopic absorption spectra of small semiconductor quantum dots (QDs) under strong confinement regime with sizes smaller than the bulk exciton Bohr radius such that the Coulombic interaction energy becomes negligible in comparison to the confinement energy. The average time rate of absorption has been obtained by incorporating the radiative and nonradiative decay processes as well as the inhomogeneous broadening arising due to nonuniform QD sizes. The analytical results are obtained for QDs duly irradiated by a strong near resonant pump and broadband weak probe. Numerical estimations have been made for (1) isolated QDs and (2) QD-arrays of GaAs and CdS. The results agree very well with the available experimental observations in CdS QDs. The results in case of GaAs QDs can lead one to experimentally estimate absorption/gain spectra in the important III-V semiconducting mesoscopic structures.