Dependence of the probability on the state of information

If the state of information changes, the evaluation of the probability also has to be modified. For example most people would agree that the probability of a car being stolen depends on the model, age and parking site. To take an example from physics, the probability that in a HERA detector a charged particle of $1\,$   GeV gives a certain number of ADC counts due to the energy loss in a gas detector can be evaluated in a very general way -- using High Energy Physics jargon -- by making a (huge) Monte Carlo simulation which takes into account all possible reactions (weighted with their cross-sections), all possible backgrounds, changing all physical and detector parameters within reasonable ranges, and also taking into account the trigger efficiency. The probability changes if one knows that the particle is a $K^+$: instead of very complicated Monte Carlo simulation one can just run a single particle generator. But then it changes further if one also knows the exact gas mixture, pressure, etc., up to the latest determination of the pedestal and the temperature of the ADC module.