Regularisation in Bayesian modelling uses classes of priors which encourage shrinkage on posterior quantities. This research proposes a new probabilistic interpretation for regularisation by way of constraints. We augment a given probability distribution with a stochastic constraint that restricts the support of the prior, emitting a "regularised" distribution as a result. This introduces the notion of probabilistic regularisation as an operator that acts on a probability distribution, rather than classes of priors which are considered to have desirable shrinkage properties. Several aspects of the so-called stochastic constraint priors are explored, including full Bayesian computation and theoretical results.