Why?
You have a dog that is male and a dog that is male or female.
In the 1/3rd scenario there is a female dog which doesn’t exist in the question. There is no female dog. There is a male dog, and a dog that is either male or female.
For the sake of the explanation, let’s say the dogs are called Rover and Spot.
From the information we have, we know that Rover and Spot are not both female. They could both be male or they could be a male and a female.
Three possibilities therefore exist:
1) Rover male, Spot female
2) Rover female, Spot male
3) Rover male, Spot male.
Assuming a random dog has a 50/50 chance of being male or female, that means the three possibilities are each equally likely to be the true position, ergo the probability of it being option 3 is 1 in 3.