In this talk, we consider a linear parabolic partial differential equation in which the control appears as a distributed source term and uncertainty acts in a structured way on the right-hand side. The objective is find a control such that some outcome of the random state occurs with maximal probability. The outcome can be enforced pointwise, for instance when requiring the state to remain bounded at every point in time and space. This type of model offers a compromise between the robust "lookback" problem and the problem of maximizing on average. Probability functions are attractive because of their interpretability, but are generally nonsmooth and nonconvex. In the case of Gaussian-like noise, the properties of the underlying control-to-state operator allow us to obtain a fully explicit formula for the Clarke subdifferential of the probability function. The formula depends on certain solutions to an adjoint equation with measures appearing in source terms. We use this formula to compute solutions in a numerical example. (Joint work with Hasnaa Zidani and Wim van Ackooij.)