For a 3-fold flopping contraction from X to the spectrum Spec(R) of a complete local Gorenstein ring (R,m) with terminal singularity at m, we give a description of a distinguished connected component of the (normalized) space of Bridgeland stability conditions on certain triangulated categories associated to the flopping contraction. More precisely, we show that the connected component is a regular covering space of the complement of the complexification of a hyperplane arrangement associated to the 3-fold flop. We also determine the autoequivalence groups of the triangulated categories. As an application of these results, we determine the Stringy K ̈ahler Moduli Space (SKMS) for all smooth irreducible 3-fold flops. This is a joint work with Michael Wemyss.