Today it was revealed that SpaceX has a deal with NASA to send a Red Dragon lander to Mars, launched on a Falcon Heavy, in 2018. The plan is that it will use supersonic retro-propulsion during the final phase of descent to slow the vehicle from about Mach 4 to 0. SpaceX's reusable first stage is the only vehicle to have ever attempted the maneuver. There have been 2 successes, and several of the failures might be survivable by a blunt body lander that can roll. But this isn't Mars, and those weren't landers.
Edit: This question is mostly about supersonic retro-propulsion. I think the crux of it is does a Falcon 9 first stage re-entering on Earth that way provide adequate data to confidently predict the same process for a blunt-body lander on Mars will succeed.
Several people have pointed out that SpaceX wouldn't do it if there wasn't a reasonable chance of success, however I think it is quite possible they would send it even if they felt it would probably crash, given that they have a large-scale, long-term business plan to settle Mars. They need the data to continue to develop the vehicle. I don't like to move the goalposts when there are already answers, but I'm changing the title to 'Is it probable', as it seems the choice of 'reasonably likely' was too open and has led to very general answers.
This paper by JPL staff seems pretty upbeat about supersonic retro-propulsion:
From 2013 to 2015, through a partnership with SpaceX, NASA received its first insight into the performance of a flight-qualified propulsion system operated into an opposing supersonic freestream. These efforts focused on analysis of SpaceX first stage recovery flight data. To return this launch stage safely to Earth, operation of its propulsion system in the supersonic regime at the right altitudes on Earth to yield Mars-relevant conditions is required. To date, SpaceX has performed SRP maneuvers during recovery operations of seven Falcon 9 first-stage systems. NASA personnel have independently reviewed these data sets. Multiple flights are in the specific Mach and dynamic pressure regime required by the present Mars EDL system. While the SpaceX first stage is not Mars-like in configuration, no showstoppers have been identified for this technology.
SRP computational, ground-based, and flight data have demonstrated that aerodynamic force and moment modeling uncertainty in the SRP phase is low for steady state, Mars-relevant conditions. Some uncertainty remains for SRP operation during startup and transition to steady-state operation, but performance uncertainty during this small time period may be mitigated by robust control system design. Combined with ground-based test data, the SpaceX flight data bounds the range of SRP thrust coefficients needed for human Mars EDL. Taken in total, these computational, ground-based, and flight test efforts significantly reduce the SRP flight system development risks for Mars EDL.
Emphasis mine. 'No showstoppers' doesn't ring with confidence. And they say data sets have been 'Mars-relevant', which isn't to say they are the same as what a vehicle entering Mars' atmosphere would experience. Based on the kind of risk assessment done for missions like this, is it genuinely probable that Red Dragon will successfully land on the first try?