This paper investigates the behavior of confined fluid in the gap between a sphere and a flat plate by examining the curve of free energy of the system versus size of the new phase. Four possible situations corresponding to new phase formation out of confined liquid or vapor at pressures above or below the saturation pressure are studied. Using surface thermodynamics, the feasible shape of the meniscus (concave/convex), the possibility of phase transition, as well as the number and the nature (unstable/stable) of equilibrium states have been determined for each of these four situations. The effects of equilibrium contact angle, separation distance of confinement surfaces, and sphere size have been studied. We show that the number and nature of equilibrium states, along with the effect of different parameters in these four possible situations, can be well described under two categories of new phase formation with (a) concave or (b) convex meniscus. Our results reveal that in the sphere-plate gap, stable coexistence of the liquid and vapor phases is only possible when the meniscus is concave (which corresponds to either capillary condensation or capillary evaporation), and when the sphere and plate are separated by a distance less than a critical amount (where that critical amount is always less than the Kelvin radius). With convex menisci, no stable coexistence of liquid and vapor phase is possible.