The evolution of scalar fields, of different initial integral length scales, in statistically stationary, homogeneous, isotropic turbulence is studied. The initial scalar fields conform, approximately, to ‘‘double‐delta function’’ probability density functions (pdf ’s). The initial scalar‐to‐velocity integral length‐scale ratio is found to influence the rate of the subsequent evolution of the scalar fields, in accord with experimental observations of Warhaft and Lumley [J. Fluid Mech. 88, 659 (1978)]. On the other hand, the pdf of the scalar is found to evolve in a similar fashion for all the scalar fields studied; and, as expected, it tends to a Gaussian. The pdf of the logarithm of the scalar‐dissipation rate reaches an approximately Gaussian self‐similar state. The scalar‐dissipation spectrum function also becomes self‐similar. The evolution of the conditional scalar‐dissipation rate is also studied. The consequences of these results for closure models for the scalar pdf equation are discussed.