Suppose that we observe a realisation $x$ of a stochastic process $X$, where $x$ is a $K\times 1$ vector taking value in $\{0,1\}^K$.
Let $\mathbb{P}$ be the probability measure associated with the probability space where the stochastic process takes place. Without further assumptions, can we write down which is the relation between $$ P \equiv \frac{\text{Number of components of $x$ equal to $1$}}{K} $$ and $\mathbb{P}$?