Why is a deterministic Turing machine a special case of a probabilistic Turing machine?
Probabilistic Turing machines are similar to deterministic Turing machines, but have the additional power of tossing coins. If you never make use of this power, you get a deterministic Turing machine.

In a similar fashion, a non-deterministic Turing machine is allowed to make guesses, but if it doesn't it is just a deterministic Turing machine.