Do you understand that "how many rolls occur after a 7 before another 7 occurs" is exactly the same as "how many rolls occur before the first 7 occurs"?

A 7 can occur on the first roll with probability 1/6 so P(x= 0)= 1/6, NOT "1 in 9".

Anything other than a 7 on the first roll has probability 5/6 and then a 7 on the second roll has probability 1/6 so .

Any thing other than a 7 on the first roll has probability 5/6, anything other than a 7 on the second roll has probablity 5/6, and then a 7 on the third roll has probablity 1/6 so .

Any thing other than a 7 on the first roll has probability 5/6, anything other than a 7 on the second roll has probablity 5/6, anything other than a 7 on the third roll has probability 5/6, and then a 7 on the fourth roll has probablity 1/6 so .

See the pattern?