Here is a very simple toy model using people with cell phones with functions and the number of digits in a phone as the total search space.
If I have 100 million or people in the US with cell phones and 10 digit numbers on each phone my chances of dialing a working number is one over 10^10 (number of possible phone numbers) minus 10^8 total people with phones.
My chance of reaching someone on the first dial is 1/100.
if I have a 13 digit number the odds decrease to 1/100000. As I now have 10^13 possible phone numbers. Exponent 13-8=5 or 10^5 or 100000
The math formula with exponents in the first case is 10^10 over exponent 10-8 or 10^2.
I hope this helps.