Systems and methods for dynamically updating user interfaces are disclosed. A system can identify a set of samples of a joint-probability distribution of a plurality of conditional events to occur during a live event, and provide a user interface for presentation at a computing device with user interface elements each indicating a respective conditional event. The system can receive a first selection of a first conditional event from the computing device, and dynamically generate, based on the set of samples and responsive to the first selection, a respective probability value for a combined selection of conditional events including the first conditional event and each other conditional event. The system can provide instructions to update the user interface to include a respective indicator corresponding to the respective probability value for each combined selection.