= Solution
Conditional on both generation-2 siblings carrying the specified copy $q$, each passes it to each of their three children with <probability> $1/2$. Their outside partners do not carry that ancestral copy. There are six independent <meioses>, one for each generation-3 individual forming the three cousin marriages. Consequently
$$
\boxed{P(\text{all six generation-3 partners carry }q\mid\text{both generation-2 siblings carry }q)=2^{-6}=1/64.}
$$
This calculation ignores <phenotype> <ascertainment in a genetic study>, as requested; conditioning on the later disease observations would force these transmissions rather than assign them their prior <probabilities>.
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