Here are the Boss Pet chances: https://runescape.wiki/w/Boss_pets
For Arraxor, the base drop chance is 1/500 with a Threshold of 200. This means, for every 200 kills, your chance increases by 1/500, and this can be increased up to 10/500.
If you have 0-199 kills, your chance is 1/500 If you have 200-399 kills, your chance is 2/500 (1/250) If you have 400-599 kills, you chance is 3/500 (1/167) .... If you have 1800+ kills, your chance is 10/500 (1/50)
Don't forget that it's a roll each time you receive the loot, and is not guaranteed - so you could technically go 10,000 kills without the pet - but I'm guessing that's why they kindly introduced these mechanics!
I have a friend who is well over two thousand kills in without the base pet drop. It's just RNG being RNG. 1/900 aren't exactly high odds, it's perfectly conceivable that you could go without it for well past the "expected" margin.
Which is a bit disheartening, sure, but then, he does have a lot of money courtesy of that dry streak.