Suppose a random number generator outputs random digits from 0 to 9. It is obvious that any given finite sequence of digits has a probability of greater than 0 to occur and it will occur infinite times in infinite number of trials.

Suppose a 2nd machine parses the output of the above mentioned machine for occurrences of the sequence 1919 and flips one of the 4 digits to 1 or 9 in random such that sequence 1919 never occurs (obviously keeping track of the immediately before digits not forming 1919). It would be logical that the probability of occurring any of the digits on the output of the second machine will be uniform and 1 in 10. So with exception of the sequence 1919 and is derivatives the sequence would satisfy the definition of a normal number, but would never include the sequence 1919.

Just trying to wrap my head around the concept of infinite random sequences.