Misleading notation in Eq. (6.32)

[houp]

Describe the mistake
In Eq. (6.32) you write "p(x_d = x_i)", which is the first (and as far as I know the last?) time you use this kind of notation, where lowercase p has an equation inside the argument. The intention is clear, but still the notation is surprising.

Moreover the usage of index "i" in x_i\in\mathcal{X} may also be misleading. In one equation we have x_d and x_i and both of these "x with an index" have a different meaning, while the symbol used is the same (one example of misleadingness can be expressed with an invalid question "Can d = i?").

Location
Please provide the

1. Draft 2024-01-15
2. Chapter 6. Section 6.4.1
3. Page 188
4. Eq. (6.32)

Proposed solution
Wouldn't P(X_d = x_i) be more readable instead of p(x_d = x_i)?

And further instead of using x_i maybe a simple x\in\mathcal{X} would be enough?