I'm certain there are several flight regimes where this could happen, and that the procedures should be different for each one. For instance, this is a very different question before lift off than it is at 100km. So, presuming that the SSMEs were burning and then all three cut out, what was the procedure at each regime, and what would have happened?
Much of the time, you would die.
Refer to the 3 OUT BLACK ZONE chart from here
The heavy black lines show where the situation is not survivable (black zone).
Acronymology for the black zone charts:
- alpha = Angle of attack
- ALT = Altitude
- c.g. = Center of gravity
- EAS = Equivalent Air Speed
- MECO = Main Engine Cutoff
- MM602 - Major Mode 602, the onboard computer operations sequence that controls the gliding portion of an RTLS
- PPA = Powered Pitch Around, the point in an RTLS where the vehicle flips over and starts flying backwards, thrusting away from the launch site to slow down
- RTLS = Return to Launch Site (an abort selectable early in the ascent in which the vehicle lands back at Kennedy Space Center)
- TAL = Trans-Atlantic Landing (an abort selectable later in the ascent in which the vehicle lands at a European airfield)
- Vi = Inertial velocity
- Vrel = Velocity relative to the launch site
The crew would select the appropriate abort procedure from this eye chart in the Ascent Checklist.
There's a lot going on here; I strongly suggest you read through the Contingency Abort document in my first link. One could literally write a book on this answer. Just as a taste, here are the definitions of the "color regions" for the three-engine out cases.