You can use -log10(1-p). On the "nines" it is exactly the number of nines you have:

    $ python3
    Python 3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0] on linux
    Type "help", "copyright", "credits" or "license" for more information.
    >>> import math
    >>> def nines(num):
    ...     return -math.log10(1-num)
    ... 
    >>> nines(.9)
    1.0
    >>> nines(.99)
    1.9999999999999996
    >>> nines(.999)
    2.9999999999999996

(Modulo floating point issues of course.)

Which then smoothly covers the entire space:

    >>> nines(.9321)
    1.1681302257194985
    >>> nines(.2)
    0.09691001300805639

But good luck getting that standardized.