The problem provided in the article and Bertrand's paradox don't seem to have "more than one answer" to me. The problems are incomplete and ill-posed. Taken to its extreme, it would be like asking: what is the probability that more than 1,000 unobservable universes exist outside of our own? So little is specified that you can't even begin to calculate a probability; the question is meaningless (particularly since there's no way to test your prediction, even in theory).