You must have smaller probes.

Hmm. Both of my 2 sets are the same size, One set is BK Precision, and the other Extech, I don't think that they're especially small - kinda standard.

If you're having problems with the probe touching other pins then heatshrink can help to insulate most of the probe. Orient the board so that you're looking face on at the pins and bring the probes in from each side - this way you're running the bottom probe through the gap and not across it.