In common law jurisdictions, the notion of proof beyond a reasonable doubt is frequently related to notions such as the belief or certainty of a judge or a juror about reality. The notion of balance of probabilities is however related to likelihood or probability. In this analysis, we link belief and proof by introducing the notion of epistemic modality, which is concerned with speaker's belief in propositional probability. The variation in the orientation of epistemic modality helps to integrate the two levels of proof and bridge the apparent test gap between them. The analysis further introduces the notion of relevance in order to clarify the nature of legal proof by taking rape cases as example. This analysis then provides an integrated language model to improve but diversify the expressions in terms of burden of proof.