Please consider $\mathbb{E}[\mathbb{1}_{A}(x)^{n-k}]$.
I am considering the expected value of an indicator to the power of $n-k$, particularly when $k=n$. I am concerned about the possibility of $\mathbb{1}_{A}(x)^{n-k} = 0^0$ in terms of whether to define $0^0 \triangleq 1$ but also how this changes the resulting probability (if defined). The indicator alone would point to contributing zero weight, but the assignment of $0^0 \triangleq 1$ would flip that to contributing non-zero weight.
What do I need to consider to resolve this ambiguity?