First problem: 3 horses participate in the race. I bet on horse number 1. Before the race, an omniscient force told me that Horse 3 would not win. Should I change my choice?
Second problem 3 horses participate in the race. I bet on horse number 1. In the middle of the race, horse number 3 breaks his leg. I have the opportunity to change my choice, but should I do it?
I understand that in first task the answer is "yes, I should". Because it's kind of Monty Hall problem. But I don't understand why the second task isn't. In both cases I recieve 100% valid information about horses. And I get these "hints" before race is finished.
So what's the difference? Does it matter when I get these hints, before the race or in the middle? Why?
According to my opinion
In both the cases the probability of winning of both the horses ( horse1 and horse2 ) are $\frac{1}{2}$ so there is no point in switching.
The main difference between Monty Hall problem and this case is that in Monty Hall problem the door in which car is present is already fixed and cannot be changed, But here horses have equal strength of winning, So winner is not fixed like before.