I believe this question is a tad bit off, or mistaken. If, such as the second example, the position were a possible but improbable en passant, then for it to qualify for the 3 fold rule, it would have to had been so from the beginning.
Three-fold repetition and en-passant

And, once again, quoting the FIDE rules: "Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same."

I believe this question is a tad bit off, or mistaken. If, such as the second example, the position were a possible but improbable en passant, then for it to qualify for the 3 fold rule, it would have to had been so from the beginning.
That answer makes no sense.

It sort of reminds me of the film Predestination, the character Jane (or The Unmarried Mother), and her consequential being. How she could not have been born without the invention of the time-machine, and yet she seemingly was. A predestined invention, a predestined child. The time machine weaves itself beautifully into every tense of time, and marks it existence by creating Jane, who is essentially a new type of existence. Cause and effect, and what is the effect without cause?
😬 I just got predestined again.

I think Wsama gave the best answer. The en passant rule is a one move rule, it cant be duplicated, so it probably would foil the 3 fold "position". So to qualify for the 3 fold rule, it would have to had been so from the beginning.

This is highly debatable even amongst arbiters. Actually most of them consider the theoretical possibilty as valid.
Same: you can't castle temporarily vs. can't castle forever
The theoretical possibilty counts in terms of the rules. Even if you can't in practise.

3 times repetition or not? In the starting position White has the right to castle but he will never do...
So 1x with the theoretical possibilty to castle (in fact he will never do) and 2x with no castling rights.

Positions are not [considered to be] the same if a pawn that could have been captured en passant can no longer be captured or if the right to castle has been changed. (FIDE 2005, Article 9.2)
Here's another good example....
In the third game of the 1971 Candidates Final Match between Bobby Fischer and Tigran Petrosian, Petrosian (with a better position) accidentally allowed the position after 30.Qe2 to be repeated three times. Play continued:
- 30... Qe5
- 31. Qh5 Qf6
- 32. Qe2 (second time) Re5
- 33. Qd3 Rd5?
and then Fischer wrote his next move
- 34. Qe2 (third time)
on his scoresheet, which is the third appearance of the position with Black to move, and he claimed a draw. At first Petrosian was not aware of what was going on. Incidentally, this was the first time a draw by threefold repetition had been claimed in his career This also illustrates that the intermediate moves do not need to be the same – just the positions.

Everyone knows that en-passant was actually introduced to chess in 2018 when the large Hadron collider at CERN after a power upgrade created a space-time bubble that merged our universe with an alternate universe that had completely different chess rules. Any reference to en-passant pre 2018 is a result of our collective memories being distorted by the trauma of being quantum entangled with another universe. A pawn in passant exists like an electron in a probability cloud, both in play and dead at the same time, until the other player acts, exerting influence on the quantum state of the board- a Schrodingers pawn if you will.

great post ghostess , that petrosian can play really good chess for a tiger cant he
Thx luv....but I just got it offa wikipaedia.

This is highly debatable even amongst arbiters. Actually most of them consider the theoretical possibilty as valid.
Same: you can't castle temporarily vs. can't castle forever
The theoretical possibilty counts in terms of the rules. Even if you can't in practise.
So what you are saying is that the rule is interpreted so that the possibility-of-en-passant-capture makes the position different, even if the capture can't actually be made due to something else? The "state" of the game, so to speak, is still different because of the en-passant possibility? We don't care if it can actually be captured or not.

But what happens if the en-passant is actually not a legal move because the king is in check, or would be put in check if the capture were done? Is the possibility-of-en-passant still considered as making the position different?
Yes, it is still considered different. The "position" definitive considers having that option. An easy way to check is to display the FEN of the board position, 3-fold repeat only applies when the same strings show up 3 times.

I think most agree to it that way. In #12 you have the castling right but you will never ever be able to do so. Same as a "pinned" ep. It is considered as having the option in terms of the rules but you can't do it.
But this is debatable, sure.
In the context of the three-fold repetition, a position is considered the same, and I quote, "if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same."
This means that, for instance, possibility of en-passant capture vs. no such possibility makes the positions different, and thus wouldn't count against the 3-fold repetition rule. Example:
But what happens if the en-passant is actually not a legal move because the king is in check, or would be put in check if the capture were done? Is the possibility-of-en-passant still considered as making the position different?