It depends on how many files there are and how the links are assigned. A security conscious developer will make the ID random for each file. The difficulty of guessing someone else's random ID is based on the length of the ID and the number of characters that make up the alphabet.
How big is the keyspace?
The link you posted has 28 characters, but you said you deleted one, so we'll call it 29 characters. We can see characters from upper and lowercase ASCII and numbers. So lets also assume the alphabet consists only of those groups. This leaves us with an alphabet size of 62 characters. To calculate the size of the keyspace we use
keyspace = (alphabet size)**(length of ID)
keyspace = (62)**(29) = 9.5358409e+51
Thats an insanely large number. So essentially you'd have to do 9.5e+51 guesses in order to find a particular file. Note that the above assumes an ID that is always 29 characters. If the ID is variable length (for example, between 29 and 50 characters), the numbers explode even more.
What is the chance I can get someone else's file?
The question becomes "If I pick a random ID what is the likely hood that I will return a file".
This question can only be answered if you know how many valid IDs there are. For the sake of simplicity, lets assume every person on the planet (7.1e+10) has uploaded a thousand files. This would mean there are 7.1e+12 valid IDs. Even if we assumed this number (and I think we can all agree that the number is much lower in reality), the likely hood of guessing a correct number would be
Likely hood of correct guess = (number of valid IDs)/(keyspace)
= 7.1e+12 / 9.5e+51
So in order to be sufficiently protected the developer should ensure:
- The keyspace of the ID is sufficiently large
- The ID is generated in a securely random way.