have a brush with (something)
To encounter, or nearly encounter, someone or something. I had a brush with death when I was in that car accident. Oh, you'll have a brush with the law sooner or later if you keep robbing houses.
have a brush with something
to have a brief contact with something; to have an experience with something. (Especially with the law. Sometimes a close brush.) Ann had a close brush with the law. She was nearly arrested for speeding. When I was younger, I hada brush with scarlet fever, but I got over it.
have a brush with
Have an encounter or come in conflict with, as in This was not the first time that Bob had a brush with the law. This expression alludes to the noun brush in the sense of "a hostile collision," a usage dating from about 1400.