P-value is the probability that the observed value (for a population of 1 groups) or difference (between groups of the population.) Provided that the null hypothesis is correct (this is seen clearly as a conditional probability)
p-value is the probability that the observed value. (For one population group) or differential. (Among the population) that provided that the null hypothesis is correct (this is clearly a conditional probability).
P-value is probability to observations (for the population 1 group) or the difference (between of population). Provided that the null hypothesis is correct (there is clearly a conditional probability)