Here's what I propose to add:

    def total(self):
        return sum(self.values())

    def scaled_by(self, factor):
        return Counter({elem : count * factor for elem, count in self.items()})

    def scaled_to(self, target_total=1.0):
        ratio = target_total / self.total()
        return self.scaled_by(ratio)

These cover the common cases and they don't mutate the counter.