probability space over the coin flips I recently read the definition of differential privacy, which is as follows: 


  a randomized function $K$ gives $\epsilon$-differential privacy if for all data sets $D$ and $D'$ differing in at most one row, and all output space $S$, we have $Pr[K(D) \in S] \leq \exp(\epsilon).Pr[K(D') \in S]$ where the probability space in each case is over the coin flips of $K$


Could somebody explain what it means when saying "probability is over the coin flip" ? an example would be greatly appreciated

Cheers
the probability space in each case is over the coin flips of K


Simply put, $K$ has values in a discrete set $\mathfrak K$ with $\Pr(K=k)=p_k$ for every $k$ in $\mathfrak K$, and
$$
\Pr(K(D)\in S)=\sum_{k\in\mathfrak K}p_k\cdot\mathbf 1_{k(D)\in S}.
$$
Similarly for $\Pr(K(D')\in S)$.
I am also confused by this expression when reading Prof. Dwork's book. I guess maybe authors only want to highlight that the algorithms discussed in differential privacy are not deterministic but probabilistic with randomization.