What role, if any, does climate change play in exacerbating the conditions for tornado formation? How is global warming changing, if at all, the map of tornado probabilities?
None that we know. The reporting database, accounting for changes in the way we collect reports, don't show trends. As the planet warms, we expect the warm, moist air to increase and the shear to decrease. It's a function of temperature gradients, which are projected to weaken as the poles warm more than the low latitudes.
As a result, one component (thermodynamics) will become more favorable and another (wind shear to start rotation of storms) will become less favorable. It's not completely clear what the sign of the overall impact on tornadoes will be, but it's likely to be relatively small.