Delaunay's proportion conjecture for p-divisible Tate–Shafarevich orders

Fix a prime $p$. For elliptic curves $E/\mathbb{Q}$ ordered by height, consider the proportion of curves for which $p\mid\#\Sha(E/\mathbb{Q})$. Delaunay's proportion conjecture. This proportion is

$$1-\prod_{i\geq1}\left(1-\frac{1}{p^{2i-1}}\right).$$

The statement is a restatement of Delaunay's preceding distribution conjecture, so it is not an independent claim; it remains heuristic and unresolved in the source.