What is the advantage of a probabilistic PKC over a traditional PKC? While reading through a textbook, I came across the idea of a probabilistic public key cryptosystem, which uses a probabilistic TM to generate the public encryption and private decryption algorithm; it is possible the encryption algorithm is probabilistic. If the encryption algorithm were not probabilistic, would the PPKC have an advantage of a traditional, non-probabilistic PKC? Can a traditional PKC offer a probabilistic encryption algorithm?
Every secure public key cryptosystem must have a probabilistic encryption algorithm.

Suppose this was not the case and consider the usual IND-CPA game.
An attacker can now win this game with probability 1 as follows:


He chooses two distinct messages $m_1,m_2$ at his liking and submits them to the challenger.
The challenger chooses a bit $b\in\{0,1\}$ uniformly at random and answers with $c'=c_b=E_{pk}(m_b)$.
The adversary computes $c_0=E_{pk}(m_0)$, if $c_0=c'$ he outputs 0, otherwise 1.
As the encryption algorithm is non-probabilistic, ie deterministic his choice for $b$ is right 100% of the time because he can be sure to always to the same value as the challenger.