Why are obfuscators generally defined to be probabilistic algorithms, rather than deterministic ones?
Let's consider the notion of IO (indistinguishability obfuscation). Informally, the definition states that for every two circuits $C_1$ and $C_2$ such that $C_1(x)=C_2(x)$ for every $x$, it holds that $IO(C_1)$ is computationally indistinguishable from $IO(C_2)$. That is, a distinguisher knowing $C_1$ and $C_2$ and given an obfuscation of one of them cannot guess which with probability greater than $1/2$.

Now, assume for a moment that $IO$ is a deterministic algorithm. In addition, assume that $IO$ does not map all equivalent $C_1,C_2$ to the same concrete output (if it could do this, then we would have an efficient way of determining that circuits compute the same function, which is co-NP complete). Then, the distinguisher could simply compute $IO(C_1)$ and $IO(C_2)$ and compare to the obfuscated program that it received. With this strategy it knows which circuit was obfuscated with probability 1. Thus, $IO$ cannot be deterministic.