= Solution
Let $(B_i)$ be a finite or countable <partition of a sample space> into <events> of positive <probability>. The <events> $A\cap B_i$ are disjoint and their <union> is $A$. <Countable additivity> and the definition of <conditional probability> therefore give the <law of total probability>
$$
\boxed{\mathbb P(A)=\sum_i\mathbb P(A\cap B_i)
=\sum_i\mathbb P(A\mid B_i)\mathbb P(B_i).}
$$
Cells of zero <probability> contribute zero through $\mathbb P(A\cap B_i)$ and can be omitted rather than assigning an undefined <conditional probability>.
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