The role of probability theory in providing information on the critical dry and wet periods using daily rainfall data was studied. The methodology was illustrated using the daily rainfall data from Kibwezi rainfall station, Kenya, with 55 years of records. The theory of runs, conditional probability, Poisson probability density and Chi-square statistics were used in the analysis. The model performed well and simulated the critical dry and wet periods (days) adequately. Results showed that one may expect the critical dry period to be about 24 and 12 days during the long and short rainy seasons, resp. Similarly, the critical wet spell is expected to last for 5 and 6 days, resp. It is suggested that drought analysis in the Kibwezi region should be based on the dry periods of the long rainy season, and runoff, soil erosion and rain harvesting analysis on the wet periods of the short rainy season.