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With the drug testing, they now do A and B samples - so if sample A comes back positive, they then test the B sample. This is an added layer to prevent the innocent being found guilty, but I guess it comes down to what made them test positive in the first place. If it's a simple dice-roll random chance thing, then the B sample is 95% likely to then prove a wrongly accused person not-guilty - but if it's something else (perhaps the drug test looks for markers in their urine which usually signify drug taking but in 5% of the population is natural), then they're still in trouble!
If it's the first case, then with a second test your 590 athletes who test positive in sample A (495 innocent, 95 guilty) becomes 115 (25 innocent 90 guilty) which gives 78% chance of getting the guilty. A bit more palatable.