Mathematics of Anonymity
An example: Suppose that only Alice, Bob, and Carol have the keys to a bank safe and that, one day, the contents of the safe are missing (without the lock being violated). Without any additional information, we do not know for sure whether it was Alice, Bob or Carol who opened the safe; the perpetrator remains anonymous. In particular, each of the elements in {Alice, Bob, Carol} has a 1/3 chance of being the perpetrator. However, as long as none of them has been identified as being the perpetrator with 100% certainty, we can say that the perpetrator remains anonymous.
Anonymity is not an absolute. That is, the degree of anonymity one enjoys may vary. In the above example, if Carol has an ironclad alibi at the time of the perpetration, then we may deduce that it must have been either Alice or Bob who opened the safe. That is, the probability of the elements {Alice, Bob, Carol} of being the perpetrator is now 1/2, 1/2, and 0, respectively. This clearly amounts to a reduction of the perpetrator's anonymity (i.e., although the perpetrator still remains anonymous, it is now more likely than before that (s)he is either Alice or Bob).
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