Historical context and the naming of specific nations in the question suggests that by is a better answer than between, in my opinion.
This seems to be a lesson in history more than English grammar. There were three heads of government (US, USSR and UK) that met at the Potsdam Conference. They agreed on dividing the city of Berlin into four zones (American, British, French* and Soviet). So, I believe the best answer is by rather than between, because it makes the statement more accurate; i.e., there would be no omission of facts with that answer (see Edit 2).
*French delegates were not at the conference, but a French zone was decided upon at the insistence of the British delegates.
Hypothetically, if the question was:
After the second world war, the city of Berlin was divided ______ the USSR, USA, UK and France.
Then, the correct answer could only be between. It could not be by in that case, because French representatives were not part of the delegation doing the dividing.
If the group of nations were less specific, e.g.:
After the second world war, the city of Berlin was divided ______ some of the victors.
Then, as Crazy Eyes pointed out, among would be acceptable. The question would be too vague though, because by could also be used to correctly answer to that question.
Between is also technically correct, because it doesn't violate any grammatical rules to say that something was divided but only list a subset of the things receiving a part of it. However, explicitly listing all but one part of the group would disingenuously imply to the reader that the list is complete. Choosing by avoids all of that complexity though, which makes it a better choice, in my opinion.