Initially it used a 386, but it and its 387 co-processor were replaced by a 25 MHz Intel-based 80486 processor system in 1999. There are also a number of 1802 8-bit CPUs onboard that control subsystems. Rad-hardened versions have a long history of reliability in space.
Once upon a time I was building test transistors for rad hard research. They had a Co-60 source to test them. So much radiation that the PFA (Teflon) holders would turn brown under the onslaught.
One night a black widow took it into her head to spin a web on the sample.
Dead the next morning, of course. When they touched her with a pair of tweezers, she crumbled to dust!
There were rad-hard versions of the 1802.
Many a geek earned their wings coding the 1802.
The problems of maintaining remote embedded systems like the Hubble are similar to maintaining implanted medical devices. They are expensive and hard to access physically so you design in failsafes, watchdogs and massive redundancy where you can. OCD afflicted coders are the sort that are needed for such work... they cannot abide any possibility of a failure and cover every contingency.