All the results of dice throws are equivalent to each other... if you pay attention and take note of EVERY die number, that is. But if you're focusing on just the number 6, then the other numbers are all considered "not 6"s.

The "not 6"s are 5 times more likely to appear than 6 on a six sided dice. The probabilities are drastically different now.

The chances of a 1 being rolled after a 6 is the same as a 6 being rolled. But the chances of a "not 6" being rolled after a 6 is much greater.

A "13554663" result is just as likely as "66666666" to occur. But if you only note the 6s, then "########" (all "not 6"s) is much more likely than "66666666" to happen because "########" fits with multiple possible results while "66666666" fits with only one possible result.