A new sub-grid-scale stochastic model of drops breakup is presented. This model describes breakup in the sample space of liquid length scales through relaxation of radius distribution function down to the long-time limit form. The last one is chosen to be a negative exponential distribution. The equation for distribution function is written in the form that satisfies long-time limit distribution. The model is implemented into KIVA-Il code with Lagrangian tracking of drop parcels. Computations of spray are performed in conditions close to those of tire diesel engine and some results are compared with spray photographic examination. Tire results show that the numerical prediction of liquid core length and spray tip penetration agree with experimental results. A broad spectrum of droplet sizes is simulated at each spray location, with coexistence of large drops and small droplets. Evolution of the shape of drop size probability density functions (PDF) at different sections in the downstream direction is shown to vary progressively toward an exponential-like distribution.