Any prize worth more than $600, the awarder of the prize is required to cut a 1099. You will pay at your marginal tax rate on the prize value. In my case, that is 35% to the Feds, 3.07% to PA, and 1% to my local township. $625 times 39% is $244, or almost a penny a mile. Not a great prize imho if the taxes are close to the true value of the miles. OK you can argue international C or F or what have you, this is why I don't fill out the UA surveys for the 100,000 mile "prize", the taxes wipe out most of the value of the prize.
Note that the above analysis ignores the effect of AMT, in other words it could be worse than my analysis if it pushes you into AMT.