Symmetries play an important role in many branches of physics and enable simplification of the mathematical description of problems. In some cases, symmetries are hidden and are only evident under suitable coordinate systems. With the help of conformal transformation, it is shown analytically here how asymmetric-looking plasmonics diabolo nanoantennas and bowtie nanocavities display a hidden symmetry that justifies the unforeseen symmetric nonradiative Purcell enhancement of a nanoemitter in their immediacy. The conformal transformation also provides physical insight on the dissimilar self-induced trapping potential experienced by such nanoemitter nearby/inside the diabolo nanoantenna/bowtie nanocavity. The analytical results are confirmed with full-wave simulations. This work highlights the elegant and cost-effective (in terms of computational burden) solution that conformal transformation provides to understand the underlying physics of and to design/model plasmonic nanostructures that are becoming key elements in sensing, quantum optics, and so on.