Cosmic rays are the only agent able to penetrate into the interior of dense molecular clouds. Depositing (part of) their energy through ionisation, cosmic rays play an essential role in determining the physical and chemical evolution of star-forming regions. To a first approximation their effect can be quantified by the cosmic-ray induced ionisation rate. Interestingly, theoretical estimates of the ionisation rate assuming the cosmic-ray spectra observed in the local interstellar medium result in an ionisation rate that is one to two orders of magnitude below the values inferred from observations. However, due to the discrete nature of sources, the local spectra of MeV cosmic rays are in general not representative for the spectra elsewhere in the Galaxy. Such stochasticity effects have the potential of reconciling modelled ionisation rates with measured ones. Here, we model the distribution of low-energy cosmic-ray spectra expected from a statistical population of supernova remnants in the Milky Way. The corresponding distribution for the ionisation rate is derived and confronted with data. We find that the stochastic uncertainty helps with explaining the surprisingly high ionisation rates observed in many molecular clouds.