You are interested in the stock of the XYZ Corporation. You feel that if the stock market goes up in the next year, the probability is 0.9 that the price of XYZ stock will go up. If the market goes down, the probability is 0.4 that XYZ will go up. Finally, if the market remains steady, the probability is 0.7 that XYZ will go up. Furthermore, you think that the probabilities are 0.5, 0.3, and 0.2 for the market to go up, go down, or remain steady. At the end of the year, the price of XYZ stock has not gone up. Given this, what is the probability that the stock market as a whole went up?