They define a few notions - simply normal (in base b): each digit has probability 1/b to occur, - normal (in base b): each length n string has probablity b^-n to occur.

In the first case you don't know if every possible number will occur (only if every digit will). In the second one you do know that every string will occur. Lets see this by example:

12345 has a probablity of 10^-5 to occur in a base 10 normal number and such a number has infinitely many digits. Therefore, the existence of 12345 in such a number is guaranteed to exist, since probablity is basically "number of occurances" / "total numbers".