In this article we suggest a definition for the notion of L1-distance that combines probability density functions and prior probabilities. We also obtain the upper and lower bounds for this distance as well as its relation to other measures. Besides, the relationship between the proposed distance and quantities involved in classification problem by Bayesian method will be established. In practice, calculations are performed by Matlab procedures. As an illustration for applications of the obtained results, the article gives here an estimation for the ability to repay bank debt of some companies in Can Tho City, Vietnam.