Stocks do the same thing, and after the split, the stock's price is determined by the market based on how much the new shares diluted the market. Seems like something very similar will happen here, with the difference being each fork will have a differing value determined by the market's exchange rate between forks?

Edit: I think many are missing the point that a fork and the original BTC blockchain are not of equal value. Maybe a more apt analogy would have been countries in the EU leaving and issuing their own currency.