Light-matter interaction is a fascinating topic extensively studied from classical theory, based on Maxwell's equations, to quantum optics. In this study, we introduce a novel, to the best of our knowledge, silver volcano-like fiber-optic probe (sensor 1) for surface-enhanced Raman scattering (SERS). We employ the emerging quasi-normal mode (QNM) method to rigorously calculate the Purcell factor for lossy open system responses, characterized by complex frequencies. This calculation quantifies the modification of the radiation rate from the excited state e to ground state g. Furthermore, we use and extend a quantum mechanical description of the Raman process, based on the Lindblad master equation, to calculate the SERS spectrum for the plasmonic structure. A common and well-established SERS probe, modified by a monolayer silver nanoparticle array, serves as a reference sensor (sensor 2) for quantitatively predicting the SERS performance of sensor 1 using quantum formalism. The predictions show excellent consistency with experimental results. In addition, we employ the FDTD (finite-difference time-domain) solver for a rough estimate of the all-fiber Raman response of both sensors, revealing a reasonable range of SERS performance differences compared to experimental results. This research suggests potential applications in real-time, remote detection of biological species and in vivo diagnostics. Simultaneously, the developed FDTD and quantum optics models pave the way for analyzing the response of emitters near arbitrarily shaped plasmonic structures.