This problem is going to produce endless fruitless debate, because, like the boy-girl problem, the specified conditions are ambiguous. The details of the randomization procedure that produced the roll with at least one 6 have not been specified, so there are at least two possible answers, depending on how the roll was produced. I would plead with everyone who is about to reply here with the answer that seems "obvious" to them to read

Wikipedia's article on the boy-girl problem first, to save a lot of pointless argumentation.

Here's one interpretation of the given problem:

"Two dice are rolled numerous times. In the cases where a six appears on at least one of the dice, the observer is told that one die is a six and asked the probability that the other is a six."

In this case, 25/36 of the rolls will not produce a six and are ignored. Of the remaining cases, 1 in 11 will have two sixes, so the answer is 1/11.

Here's another interpretation of the problem:

"Two dice are rolled once. It just so happens that at least one die shows a six. The observer is asked for the probability that the other is a six."

In this case the probability that the second die is a six is the same as the probability that any arbitrary thrown die is a six, 1/6.

Clearly different people in this thread are already interpreting the problem in different ways, and therefore producing different results.

--Mark