The most recent measurements of comet C/2013A1's orbit show it will pass roughly 37,000 km from the surface of Mars next year. Uncertainty of the orbit still leaves a small chance of a direct impact.
That's a little bit farther out than asteroid 2012DA14 passed from Earth, but this comet is much larger. But, A1s coma should be ~100,000 km in diameter by the time it reaches Mars's orbit.
Even if the nucleus does not impact, Mars will still be passing through the coma and be subjected to some degree of bombardment, including objects large enough to pass through the Martian atmosphere and pose a danger to probes in orbit and on the surface - we don't know how dense the meteor rain from a coma passage like this would be.
If the probes survive, it's hoped they'll be able to get images of the comet as it passes, since it'll dominate the sky for several days and completely fill it at closest approach.
In the event of an actual direct impact, probes on the surface will almost certainly be lost. The current size estimate range is 15-50km. At 15 km it'd already be one of the largest comets to pass through the inner solar system, and at 50 km it'd be second only to Hale-Bopp.
For example, News.com.au was one of the first outlets to post this story, and it showed Earth as the target for two weeks before they corrected it. From there it of course entered the blog rotation from which misinformation is impossible to remove, supposedly it's currently got the most traction in the Russian parts of the internet, which have always been one of the breeding grounds for stuff like this but a bit worse than usual in the wake of the Chelyabinsk impact.
Tis the end of the world, that calls for a drink!!
How many times is the world supposed to end this year anyway?
This year's doomsday schedule is comet C/2012 S1 ISON, which should be spectacular in November/December if it survives sungrazing first. It made the conspiracy circuit last year since people saw ISON as an abbreviation or anagram for things concerning Nibiru or the Second Comming.
Then there's a generic "all year" prediction from somebody who reevaluated Newton's 2060 prediction and believes he was wrong and it's 2013.
If it's at the lowest range of its size, chances are already slim that any of the probes would survive, no matter where the impact is - that's 1.5-2x the size of the Chicxulub impactor on smaller planet with a thin atmosphere, it will be a global event.
If it's towards the upper range of size, though, the rovers are lost, period, no matter where they are. There's even concern that some of the orbiting probes will be in danger, since some of them are as low as 300-400 km. A 50 km impactor would create a crater larger than most known on any body in the inner solar system. The impact on Mars would be unbelievable.