Three fair coins are tossed behind a screen. You are told only that at least one of them came up heads. What is the probability that all three came up heads?

The 8 equally likely outcomes lose exactly one member, TTT, once you know at least one head appeared, leaving 7 possibilities. Only HHH has all heads, so the probability is 1/7. Trap 1/8 answers the unconditional question and wastes the information given. Trap 3/8 is the chance of exactly two heads. Trap 7/8 is the probability of the CONDITION itself (at least one head), not of the event asked about.