Predicting an uncertain future with uncertain knowledge is a challenge. The success of efforts to preserve biodiversity, to maintain biosecurity and to reduce a negative impact from climate change, depend on scientifically based predictions of future events. The ongoing introduction of non-indigenous species threatens ecological systems for which empirical data is sparse and scientific knowledge is uncertain. Since biological invasions constitute a type of risk characterized by small probability events with possible large consequences, the use of subjective judgements and how knowledge based uncertainty are dealt with is a critical issue. In this thesis I do case studies of probabilistic analysis of biological invasions with the purpose to get more insight into what it means to predict future events under uncertainty and go into the methodology of probabilistic analysis, with special focus on risk analysis of biological invasions. In the first study I produced an overview to probabilistic models of establishment success. I found that probabilistic models for a common endpoint can be different, depending on how the endpoint event is measured and the type of available data. In study two to five I quantified uncertainty in some relevant biological invasion endpoints, using empirical and artificial data and probabilistic analysis. From these studies I learned that a probabilistic model estimated with empirical data is information on the goodness of the model to describe the world, whereas the same probabilistic model is information on the uncertainty in the future event. I find information theoretic approaches as suitable to derive good models, and Bayesian approach as suitable for combing various sources of knowledge into predictions. At the end, I discuss what it means to predict uncertainty under uncertainty using probabilistic analysis for various strengths of background knowledge.