Chance of contamination once FG is established?

What is the chance for contamination if beer has fermented from 51 down to 11? Basically I took three reading in three days and it is staying right at 11. My concern is i did not sanitize my hydro tube that came in contact with my cane that I used to pull from the carboy. I had to draw eight canes worth each time to fill enough for the readings. Am i a paranoid freak that needs to invest in a thief? It might be over the top, but I just cannot help but think i messed up. Thanks for all the replies.

It will probably be alright. Beer is less of an infection risk than wort. Heck, I once dropped a [relatively clean] paper towel in cooled wort and the beer didn't get infected. In general though, it's best to sanitize anything that comes into contact with wort or beer.