Coin flipping

#1
Alan, Bob, and Charlie agreed that the “odd man” (the person whose outcome is
different from others) would buy the coffee. After simultaneously flipping their
coins, Bob turned up with the only “tail”. At this point Bob demanded to Alan’s
and Charlie’s coins. He discovered that Alan had used a two-headed coin. With
this Bob accused Alan of cheating and refused to buy. Charlie, however, insisted
that even with Alan’s suspicious coin the game was fair and therefore Bob was
obliged to buy. Under the circumstances, what was each man’s probability of
losing? Do you agree with Charlie?

This was the question. I was thinking since Charlie has two headed coins, the total combination for all players should be 2x2 =4. The results would be:
HHH, HTT, HTH, HHT
According to this result, all players have an equal chance of winning. (Probability of 1/4). This is was I thought. Not quite sure if this is the correct logic. A guide is needed. Thanks.