Climate policy decisions driving future greenhouse gas mitigation efforts will strongly influence the success of compliance with Article 2 of the United Nations Framework Convention on Climate Change, avoiding "dangerous anthropogenic interference (DAI) with the climate system". However, success will be measured in very different ways by different stakeholders, suggesting a spectrum of possible definitions for DAI. The likelihood of avoiding a given threshold for DAI is dependent in part upon uncertainties in the climate system, notably, the range of uncertainty in climate sensitivity. We combine a set of probabilistic global average temperature metrics for DAI with probability distributions of future climate change produced from a combination of several published climate sensitivity distributions and a range of proposed concentration stabilization profiles differing in both stabilization level and approach trajectory,including overshoot profiles. These analyses present a "likelihood framework" to differentiate future emissions pathways with regard to their potential for preventing DAI. Our analysis of overshoot profiles in comparison with non-overshoot profiles demonstrates that overshoot of a given stabilization target can significantly increase the likelihood of exceeding "dangerous" climate impact thresholds, even though equilibrium warming in our model is identical for non-overshoot concentration stabilization profiles having the same target.