Prevention of voltage instability in electric power systems is an important objective that the system operators have to meet. Under certain circumstances the operating point of the power system may start drifting towards the set of voltage unstable operating points. If no preventive measures are taken, after some time the operating point may eventually become voltage unstable. It will thus be preferable to have a measure of the risk of voltage collapse in future loading states. This paper presents a novel method for estimation of the probability distribution of the time to voltage instability for a power system with uncertain future loading scenarios. The method uses a distance from the predicted load-path to the set of voltage unstable operating points when finding an estimate of the time to voltage instability. This will reduce the problem to a one-dimensional problem which for large systems decreases the computation time significantly.