Feel a bit cheeky for asking, but I'd appreciate some opinions on a debate that has come up where I work.
If you know that something cannot happen, is it approriate to say that it has a probability of zero, or is probability an inapproriate concept in that situation.
I would say the following (a physicists perspective maybe): Saying something cannot happen and assigning a probability of zero to that event are exactly identical. One might argue that it is pointless to do so but such a zero probability can have some merit. For example: In quantum mechanics you will express the probability for a system for going from state a to state b, which would read (in qm notation): P(a->b)=C*< a|H'|b > where basically a and b are the functions describing states a and b and H' describes the way in which the system is being influenced. The construct <|> is just a short notation for a certain mathematical operation (taking the complex conjugate of a multiplied by the operator multiplied by b and integrating over R3 usually). Such a probability can turn out to be exactly zero for two given states a and b (not approximately but exactly). This then basically tells you that your system will not change from a to b (or vice versa) for the stimulus provided (which is described by H'). So a probability of zero can make a lot of sense...
I can see that a result which produces a probability of zero is useful.
I'm talking more about assigning a probability (or liklihood) of zero (or one) to some event, rather than determining via probabilites that something has zero probability.