[fela]

The definition of p-value is the same independent of method, as far as I can tell the only real difference is that by Neyman–Pearson you just look at whether the p-value is below a threshold, and Fisher looks at p-value as "strength of evidence" valuable in itself. It's still not the probability that your result was due to chance, it's the probability that under the null hypothesis (and you will definitely need one) you would get that value (or more extreme) by chance.