If a person is infected with HIV is it possible to get infected if I rinsed his toothbrush in the sink and some of the water splashes into my eyes?

Extremely unlikely. In some persons living with hiv, the virus has been detected in saliva, but in extremely low quantities. Contact with saliva alone has never been shown to result in transmission of hiv, and there is no documented case of transmission from an hiv-infected person spitting on another person. If tainted with blood it increases the chances but extremely unlikely. If concerned, get tested.
Low risk.. The risk is low... To ease your mind you can get tested...
Highly unlikely. Still to my knowledge there has been no reported incident of saliva contamination that caused hiv...It is extremely unlikely, however if the tooth brush had a lot of blood on it, it could be considered a little more possible, but again still very very unlikely. If truly concerned, consult with your physician. If this is a work related incident, then your employer will need to help.