SOLUTION: toss a fair coin three times, the conditional probability of having one head given that the first outcome is a tail is

To be clear, the word "EXACTLY" or the words "AT LEAST" should be in there.

But regardless, the complete sample space of tossing three coins in 
succession is:

{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} <--complete sample space

Also, regardless, the reduced sample space for the GIVEN part, that the 
first outcome is a tail, is this reduced sample space of the 4 possible 
cases when the first outcome is a tail:

{THH,THT,TTH,TTT} <--reduced sample space

If your problem should have read:

then there are 2 successful ways, THT and TTH to have EXACTLY one
head out of the 4 possible ways {THH,THT,TTH,TTT} of having a
tail first.

So the probability is 2 ways out of 4 or 2/4 which reduces to 1/2.

However, if your problem should have read:

then there are 3 successful ways, THH, THT and TTH to have AT LEAST one
head out of the 4 possible ways {THH,THT,TTH,TTT} of having a
tail first.

So the probability in this case is 3 ways out of 4 or 3/4.

Edwin