You can argue that either; pressure does not change the amount the [a non-radioactive] air ionises, because the ionisation is a result of ionising radiation from an external source, which is independent of the pressure
or; probability of ionisation within a small volume is proportional to the mass in that volume (on account that if there is more mass there, then it is proportionally more likely to respond to incoming radiation).
Once ions or electrons are present, then the application of an electric, or time-varying magnetic, field may cause acceleration of those ions/electrons that then go on to cascade further ion production. You therefore have two mechanisms - an initial ionisation from radiation, then ionisation from accelerated charged particles. The latter is affected by the pressure according to some very complex phenomena which you can research by looking up 'Pachen breakdown', and the long-and-short summary is that it is to do with mean free paths and whether the particles can pick up enough energy to produce more charged particles before they get 'neutralised'.