Various mechanisms have been proposed to explain the nonphotochemical laser-induced nucleation (NPLIN). Identifying the dominant mechanism requires addressing a large set of experimental parameters with a statistically significant number of samples, forced by the stochastic nature of nucleation. In this study, with aqueous KCl system, we focus on the nucleation probability as a function of laser wavelength, laser intensity, and sample supersaturation, whereas the influence of filtration and the laser-induced radiation pressure on NPLIN activity is also studied. To account for the nucleation stochasticity, we used 80-100 samples. The NPLIN probability showed an increase with increasing laser intensity. The results are different from the previous report, as a supersaturation independent intensity threshold is not observed. No dependence of the NPLIN probability on the laser wavelength (355, 532, and 1064 nm) was observed. Filtration of samples reduced the nucleation probability suggesting a pronounced role of impurities on NPLIN. The magnitude and the propagation velocity of the laser-induced radiation pressure were quantified using a pressure sensor under laser intensities ranging from 0.5 to 80 MW/cm². No correlation was found between the radiation pressure and NPLIN at our unfocused laser beam intensities ruling out the radiation pressure as a possible cause for nucleation.