The distribution of liquid water in ice-free clouds determines their radiative properties, a significant source of uncertainty in weather and climate models. Evaporation and turbulent mixing cause a cloud to display large variations in droplet number density, but quite small variations in droplet size (Beals et al., Science, 2015, vol. 350, pp. 87-90). However, direct numerical simulations of the joint effect of evaporation and mixing near the cloud edge predict quite different behaviours, and how to reconcile these results with the experimental findings remains an open question. To infer the history of mixing and evaporation from observational snapshots of droplets in clouds is challenging, because clouds are transient systems. We formulated a statistical model that provides a reliable description of the evaporation-mixing process as seen in direct numerical simulations and allows us to infer important aspects of the history of observed droplet populations, highlighting the key mechanisms at work and explaining the differences between observations and simulations.