A black swan is a high-impact event that is hard to predict (but not necessarily of low probability). Also, an event that is not accounted for in a model, and therefore causes the model to break down when it occurs.

Labeling some event a black swan, doesn't mean you can't assign any probabilities, since making decisions depending on the plausibility of such event is still equivalent to assigning probabilities that make the expected utility calculation give those decisions.

External posts:

White Swans Painted Black by Peter McCluskey

See also

Narrative Fallacy
Hindsight Bias
I Don't Know
Forecasting & Prediction, Prediction Markets, Forecast