Completely normal, if you're not using a probe with a sufficiently short ground spike. If you're using the standard croc clip lead, which adds a few inches' worth of inductance to your ground connection, then that's exactly the sort of poor signal integrity and crosstalk you can expect.
With your probe's accessory kit there should be a short ground spike made of spring steel. Remove the croc clip lead, install this on your probe tip, and try again with the tip of the spike touching a ground point somewhere within, say, 10mm of the signal you're looking to probe.