Process mining, when applied to data stored in the information systems of businesses, provides insights into the internal performance of their processes. These insights reveal how the behaviour of processes impacts businesses, and can inform planning for various future scenarios by anticipating how processes will perform in these scenarios. However, these scenarios may be influenced by the context of the process, i.e., external data streams (exogenous data) to the process. In these cases, typical process discovery techniques can produce process models that describe what activities could occur next in a given state, but cannot express the effect of external influences on how likely these are to occur. Our contribution presents an extension of stochastic labelled Petri nets and a discovery technique for our new modelling formalism. The proposed formalism can be used to quantify whether the firing likelihood of a transition is influenced by exogenous data when replaying historical process executions over the net. We compare our approach against existing stochastic techniques over several publicly available event logs. Our results show that our approach can outperform existing data-aware techniques in unstructured processes.