The expression for the probability density function of scalar field pulsation values is derived taking into account the fractal and multiscales structure of turbulence. The evolution of this function was stated by the detailed structure of the probability distribution of length scales of a scaler turbulent field. The expression for the latter has been found using the fractal character of the surfaces separated the regions with the different scalar concentrations in turbulent flows. Analytical expressions for the conditional dissipation rate of scalar fluctuations were proposed using the hypothesis on typical realisations of a scalar turbulent field which were different at various evolution stages. It is possible to consider these expressions as an attempt to explain a sufficiently complicated transformation of the form of conditional dissipation, which were obtained by direct numerical simulation of a turbulent scalar field. The obtained analytical expressions for a conditional dissipation rate can be useful to study the turbulent combustion process in the framework of the laminar diffusion flamelet models.