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I have been scratching my head trying to work this problem out myself - with little joy I might add. So I am asking for help, please.
If the best horse in the race has a 50% channce of winning the race, what is the probability the horse will finish in the first three places? Assume there are 8 runners in the race.
Either .643 or .875. The only given info you have is 50% chance of winning, and 50% chance of losing or getting 2nd, 3rd, 4th, 5th, 6th, 7th, or 8th place. If getting 2nd is just as easy as getting 8th (unlikely) then that 50% gets divided evenly for a 7.14% chance of getting one of those finishes. That is how I get .643. Another way to look at is 50% shot of getting 1st place. To get second is then a 25% chance, and 3rd is 12.5% chance...
Colby has provided some interesting conclusions based on sufficiently disclosed assumptions, but really, there just isn't enough information. You must make some sweeping assumptions to get any answer at all. After making sweeping assumptions, what have you accomplished? Pretty much nothing.
It's something greater than 50%. THAT can be said.