Polar vortex is a strong jet of westerly wind which forms each winter around the polar stratosphere. Sometimes, roughly every other winter, the polar vortex in the Northern Hemisphere experiences a dramatic breakdown and associated warming of the polar stratosphere. Such events are called sudden stratospheric warmings (SSW) and they are known to have a significant influence on ground weather in Northern Eurasia and large parts of North America. Typically, these events are thought to occur due to planetary waves propagating to the stratosphere where they may disrupt the vortex. Here, we show that the SSW probability depends significantly on a favorable combination of geomagnetic and solar activity and the phase of the Quasi-Biennial Oscillation (QBO). Using logistic regression models, we find that more SSWs occur when early-winter geomagnetic activity (aa index) is low and QBO winds are easterly and when solar activity (F10.7 index) is high and QBO winds are westerly. We then examine the possibility of using these results to predict the occurrence probability of SSWs with several months lead time and evaluate the optimal lead times for all variables using cross-validation methods. As a result, we find that the SSW probability can be predicted rather well and we can issue a probabilistic SSW prediction for the coming winter season with a success rate of about 86% already in the preceding August. The results presented here are an important step toward improving the seasonal predictability of wintertime weather using information about solar and geomagnetic activity.