Active distribution networks are promising to provide ancillary services to the utilities in addition to traditional generation. The idea is to make use of the controllable distributed energy resources within the distribution network to regulate the power exchange with its upper level grid on the basis of a set point determined by the utility. However, determining an interval of feasible set points for this power exchange is challenging because of the uncertainty affecting the uncontrolled generation and demand. This paper proposes a novel methodology to compute feasible variability ranges for the power exchange with the upper level grid. In particular, the method seeks for the range maximizing the probability that a set point within the range is feasible, given a realization of the uncertain generation/demand. The proposed method combines numerical optimization and probabilistic forecasts with concepts from the theory of multi-parametric programming. Simulations based on a modified European CIGRE Low Voltage benchmark grid are used to illustrate the proposed findings.