The answer was 3 in 80, or 3.75%
Discussion
Show the math!
There are 2 die rolls, a d20 with range 1-20, and a d4 with range 1-4. Between them there are 20x4 (80) combinations of possible results.
To succeed on the check, the combined total of dice rolls and the modifier (-1) must be 22 or greater.
The following 3 dice combinations result in success:
> 19 + 4 (totals 23, minus 1 = 22)
> 20 + 3 (totals 23, minus 1 = 22)
> 20 + 4 (totals 24, minus 1 = 23)
with 3 succesful combinations of 80 possible, this yields a percentage success rate of 3/80 or 3.75%
3 valid combinations. I somehow got it in my head that there were 4. I blame working it out in bits and pieces around real life's constant intrusion on my fun.