It depends on if you think of poker as a game of luck or skills.
When you have a six side dice the probability of getting the number 6 is 1/6
because all the sides are exactly the same.
If you cheat and make a dice with one side heavier the probability of getting 6
would be different because the sides are different.
So in the game flip , where all the players go all-in they have the same chances
as they behave exactly the same,
but in a regular rules game you may expect the players of
different skills, hence their chances are different than 1/(number of players).
But if you say that in poker all is just luck, then yes all players have the same chances to win.
However if the skill matters ( at least a little ) the more experienced player has better
odds.
Similar if you put Negreanu,Hellmuth and Ivy behind the table and ask them to play each one has
the chance to win of 1/3 only if you think that they are on the same level ,
but if either one is more skilled he would have a better chance.