3.6 Conditioning on the past and future

A useful application of conditional probability is to condition on possible outcomes of future events to see how this affects probabilities of interest. For example, banks who lend money will need to consider the probability that loanees will be able to repay that money (with interest). A future event which would affect that probability could be the lonees’ employment status. If their employment is unstable and their probability of repayment would greatly decline if they were to lose their job, then the bank might be less likely to lend to them compared to if their probability of repayment was unaffected by their employment status (e.g. if they own physical assets that the bank could seize if they fail to repay). Considering possible future events and risks helps to make uncertain decisions in the present.

We can also condition on possible events in the past. This is useful for example when the causes of past events are unknown. This is epistemic uncertainty. In this case, we can consider the probability of the observed outcome conditioned on multiple candidate causal events. These conditional probabilities can then be compared to determine the support of each of the causal events for the observed outcome. This is how conditional probabilities are used for interpreting forensic evidence: we look at the events which the defence and prosecution assert and compare how likely the observed evidence would have been when it is conditioned on each hypothesis. For example, when interpreting fibre evidence recovered from the clothing of a person of interest, the expert must consider how probable this evidence would have been in light of what both the prosecution and defence claim to have happened.