Captain Janeway would get Naomi Wildman, Neelix, Treevis, Flotter, Leonardo Da Vinci, and 7 of 9 together to come up with a plan involving the Delta Flyer and Chakotay's medicine wheel to render the probe inert. She'd also make sure nothing happened to her lucky mug.
Sisko would tell the probe that it's not linear. Because he can live with it... he CAN live with it.
Picard would fly the Enterprise into the nexus, meet up with Captain Kirk, and inform him that they have to find a pair of humpback whales... they have to stop an alien probe before it destroys the Earth. Kirk would reply that he takes it the odds are against us, and the situation is grim, and that it sounds like fun.
Non-Trek: Captain Sheridan would begin a monologue, which would put the probe to an eternal sleep.
Non-Trek: Admiral Adama would simply shoot the probe an intense glare, which would result in the probe's instant and total self-destruction.
Non-Trek: Commander Sinclair would take a Starfury to the probe, and upon seeing the destruction being wrought upon the Earth would say "Not like this, not like this... if I'm going I'm taking you bastards with me!", and set his Starfury for a full-velocity ram, at which point the probe would tractor him, as the whales realize he is the One.