The classic scientist algorithm "That's odd, we should assign some resources for more study"
The tricky bits are buried in how exactly do you define "odd", "some" and "resources" ?
Starting with the the point that one persons outlying (but valid) observation is another persons probable instrument error.
And that's the easy part. You can just crunch it overnight on a NASA server farm.
The SoA for on board space computers is roughly a Power PC running about 400MHz flash drive (NASA never seemed to like spinning rust on orbit). Capacity isn't too much of a problem but main memory is also fairly limited. I'm not sure if NASA has run any GPU's or GPU arrays on orbit yet. Very handy to have in this sort of situation but difficult to get in rad hard Mil Spec versions.
Keep in mind that beyond Jupiter by the time a probe has sent back a report of something interesting and NASA has a)Agreed it is interesting and b)What to do about it
the phenomena could have disappeared. If the mission is a flyby then the probe may already have gone past it.