Who let pet name this shit 🙏

LMAAO

If assuming caps doesn't matter, about 1 in 238328.
Source: discord.gg links apparently use the RegEx [0-9A-Za-z]{10}, which can match any of those 62 characters ten times. The f slur is shortened to 3 letters, thus the chance of it appearing in the link (regardless of capitalization) is 1 in 62^3, or 1 in 238328.

Of course I might be under-researching this and discord.gg links can have more than just the 62 char set.

???