The probability distribution, in space, of a passive scalar advected by a model, divergence‐free, velocity field is analytically calculated. It is found to have a logarithmic singularity at the origin and a quasi‐Gaussian decay away from it. The significance of this result for the general case of convection of passive scalars and the relation to a recent theory of Yakhot and Sinai [Phys. Rev. Lett.63, 1962 (1989)] are discussed.