@J.M. for instance, given `\[Mu] = Table[i, {i, 5}]; S =
Table[i + j, {i, 5}, {j, 5}]/20 + DiagonalMatrix[Table[1, {5}]];
Clear[pdf]; pdf = MultinormalDistribution[\[Mu], S];` the command `cpdf = ConditionnalMultinormalDistribution[
pdf, {x2, x3, x4, x5}, {2, 3, 4, 5}];
PDF[pdf, {x1, x2, x3, x4, x5}]/PDF[cpdf, x1]/
PDF[MarginalDistribution[pdf, {2, 3, 4, 5}], {x2, x3, x4,
x5}] // Simplify` should return 1