The probabilistic consideration of the global pairwise sequence alignment of two RNAs tied with their global single secondary structures, or global pairwise structural alignment, is known to predict more accurately global single secondary structures of unaligned homologs by discriminating between conserved local single secondary structures and those not conserved. However, conducting rigorously this consideration is computationally impractical and thus has been done to decompose global pairwise structural alignments into their independent components, i.e. global pairwise sequence alignments and single secondary structures, by conventional methods. ConsHomfold and ConsAlifold, which predict the global single and consensus secondary structures of unaligned and aligned homologs considering consistently preferable (or sparse) global pairwise structural alignments on probability respectively, were developed and implemented in this study. These methods demonstrate the best trade-off of prediction accuracy while exhibiting comparable running time compared to conventional methods. ConsHomfold and ConsAlifold optionally report novel types of loop accessibility, which are useful for the analysis of sequences and secondary structures. These accessibilities are average on sparse global pairwise structural alignment and can be computed to extend the novel inside-outside algorithm proposed in this study that computes pair alignment probabilities on this alignment.