This isn't being fair. I don't really think the post title is fair either. That 93% isn't comparable to the 50% you're probably thinking for the coin flip, or even the 0/100% mentioned in your edit.
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93% alert rate means:
93% = false positive + true positive
7% = true negative + false negative
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We're given "His success rate was much lower, at 59 percent." Assuming that means that 59% are true positives, we know the false positive rate is 34%.
Without data on how many passengers are carrying drugs, we can't say anything about the rest of that result. A plausible world where the drug dog may be valuable is when he unquestionably rules out that 7% of the population that he doesn't alert on, as in false negative = 0.
I believe the reason this number is so high (59%) is that the officer has already used his suspicion to determine filter out most people. This makes the value of the "ruling out" plausibility even more valuable: the drug dog reduces searches compared to trusting the cop.
Ideally, they'd provide the receiver operating characteristics curve [0] or the confusion matrix [1].
[0] https://en.wikipedia.org/wiki/Receiver_operating_characteris...
[1] https://en.wikipedia.org/wiki/Confusion_matrix