I myself would say unhesitatingly that a third of the pie each, is fair.

That's the default with no additional data, but I would hesitate, because to me how much each of the persons need the pie is also important in defining "fairness". If one of the three is starving while the others two are well-fed, it would be fair to give more to the one starving.

It may be just nitpicking, but since you took the point to ensure there is no difference between the three characters are involved in spotting the pie, but not mentioned they have the same need of it, it may pinpoint a deeper difference between different conceptions of "fairness" (should give them two different names ?)