= Solution
The first 12 weeks are in custody and carry no stated overdose deaths. Thus the 26-week sentence-based window includes 14 weeks after release: the first two weeks followed by the next twelve. Interpreting the later <probability> conditionally on surviving the earlier interval gives
$$
p_A=\frac1{200}+\left(1-\frac1{200}\right)\frac1{250}=0.00898.
$$
Hence
$$
\boxed{\mathbb ED=10{,}000(0.00898)=89.8\ \text{deaths, approximately }90.}
$$
If the two quoted frequencies instead use the same original cohort as their denominator, add the two marginal <probabilities> to get exactly 90 expected deaths. The conditional-survival calculation makes the denominator interpretation explicit; both conventions agree at the rounded precision of the quoted rates.
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