Find the probability of the situation where we have 1 byte(8 bit) and there are no any 3 equal bits sequence in this byte. All values of the byte are equiprobable. I`ve tried to find the inverse probability, but i even do not know what is easier to perform. Also I made a binary tree of these byte and find out that probability is 26-27%, but it was bruteforce count. There are much more techniques that i've tried, but they won't help to find the solution.
To be clear, i`ll show the example:
$10101011$ - is ok
$10111000$ - is not ok, there are $111$ and $000$