So you go to the docs and the doc says, I got your test results back. I'm really sorry but you tested positive. But there's some hope because only a third of those who test positive actually have the disease. But using your argument, you say ... don't worry doc. My odds of having the disease were 1 in 100 before you told me the result. And the fact that you are telling me I've tested positive changes nothing. My odds are still 1 in 100. So I have very little to worry about

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The point is the conditions are quite different to the one you are pointing to. Therefore the odds are different.
Suppose you bet on a horse in a race taking place in three weeks and you get 3-1 odds. However, it rains heavily overnight so the going on the day of the race is heavy and your horse doesn't do well on heavy ground. Thus the odds of your horse winning change - and no doubt reflected in the bookies prices as other punters realise this.