Using off-lattice Monte Carlo simulation, we investigate the effects of topological constraints on the free energy and metric properties of an unknotted ring polymer without exclude volume interactions confined in a slit with width d, as well as the effect of confinement on the probability of forming an unknot in a freely jointed ring. Because of the topological constraints, the polymer size of an unknotted ring is shown to behave differently from that of a freely jointed ring: the in-plane radius of gyration R-g parallel to increases with increasing confinement. However, the free energy of an unknotted ring follows the same scaling law as a freely jointed ring for strong confinement. This abnormal phenomenon is explained on the basis of the fact that the length of subchains inside the confinement blobs is smaller than the topological blob size, i.e., the characteristic length below which topological constraints become unimportant. As in the bulk, the probability of forming an unknot decreases exponentially with the chain length, but the decay length decreases with decreasing confinement length. We propose an efficient method for calculating the probability of forming unknot from a freely jointed ring in confinement.