This is ambiguous and the language can be interpreted in at least three ways.
1) you flipped two coins. One of them was heads. Let's mark that one with red tape. Let's mark the other with green tape. What is the probability of the one with green tape is also heads.
This is basically how you interpreted the problem. It seems a linguistically fair way to interpret it.
2) You flip two coins. I call you up and say. "Hey, is at least one of the coins heads?" You look and correctly say "yes". I ask "is the other one heads?" You answer correctly.
What is the probability you said yes.
The answer is 1/3 for the reason the book gave.
This is what the book meant. It represents a basic lesson in conditional probability.
But it's a linguistic nightmare. "One lands head" ="at least one is heads" is fine but then "the other one" forces us to inaccurately declare we had one coin in mind when we said "one was heads" when we didn't
3) you flip two coins. One lands heads. It's not that zero landed heads. It's not that two landed heads. One landed heads.
What is the probability the other is heads?
Answer: 0, of course.
Perhaps this could be better stated as:
You flip two coins. You get at least one head. What is the probability that both are heads.
I leave you with a joke.
In American currency we have the following coins: pennies worth $1$ cent, nickels worth $5$ cents, dimes worth $10$ cents, and quarters worth $25 $ cents.
I have two (American) coins. They add up two 30 cents. One of them is not a nickel. How is that possible?
Answer: The one that is not a nickel is a quarter. The one that is a nickel is a nickel.
 there are four ways a coin can land.
HH, HT, TH, TT. But one of them is not possible.
The three possible ways are HH,HT,TH and they are equally likely. Of those three ways in only one of them is "the other coin" heads.