The p-value is the probability that the null hypothesis is true. Here for instance, the null hypothesis has only a 1.3% chance of being true.
The p-value for the null hypothesis is the probability that chance alone produced the observed effect. Here for instance, there is an 1.3% probability that chance alone produced the effect (i.e., the difference).
The p-value is the chance of our data occurring if the null hypothesis is true. Here for instance, p = 0.013 means that the observed difference would occur only 1.3% of the time under the null hypothesis.