  A longstanding question in stellar evolution is which massive stars produce
black holes (BHs) rather than neutron stars (NSs) upon death. It has been
common practice to assume that a given zero-age main sequence (ZAMS) mass star
(and perhaps a given metallicity) simply produces either an NS or a BH, but
this fails to account for a myriad of other variables that may effect this
outcome, such as spin, binarity, or even stochastic differences in the stellar
structure near core collapse. We argue that instead a probabilistic description
of NS versus BH formation may be better suited to account for the current
uncertainties in understanding how massive stars die. We present an initial
exploration of the probability that a star will make a BH as a function of its
ZAMS mass, $P_{\rm BH}(M_{\rm ZAMS})$. Although we find that it is difficult to
derive a unique $P_{\rm BH}(M_{\rm ZAMS})$ using current measurements of both
the BH mass distribution and the degree of chemical enrichment by massive
stars, we demonstrate how $P_{\rm BH}(M_{\rm ZAMS})$ changes with these various
observational and theoretical uncertainties. We anticipate that future studies
of Galactic BHs and theoretical studies of core collapse will refine $P_{\rm
BH}(M_{\rm ZAMS})$ and argue that this framework is an important new step
toward better understanding BH formation. A probabilistic description of BH
formation will be useful as input for future population synthesis studies that
are interested in the formation of X-ray binaries, the nature and event rate of
gravitational wave sources, and answering questions about chemical enrichment.
