Freezing of evaporating cloud droplets by homogeneous nucleation is an important mechanism for ice formation in the atmosphere, but it has been studied very little. Extension of the standard theory of homogeneous freezing to evaporating conditions results in an analytical expression for the freezing probability. A dimensionless freezing number F_h characterizes the process and is found to be proportional to the fifth power of the initial drop radius. For any finite value of F_h , the derived expression predicts that only a fraction of any uniform drop population will freeze, regardless of the time available. New laboratory measurements of individual droplets levitated electrodynamicaly confirm the essential features of the expression and yield nucleation rates that are consistent with those determined by others.