This work presents the design and simulation of a high-voltage probe intended for measuring extremely fast electrical pulses with high accuracy. Such measurements are particularly important in advanced applications including plasma diagnostics, pulsed laser systems, and high-power microwave technologies fields where signals often rise and fall within nanoseconds or even picoseconds. Conventional probes and oscilloscopes struggle in these conditions because of bandwidth limits, high cost, and susceptibility to interference and parasitic effects. To address these challenges, a compact and cost-effective capacitive voltage divider (CVD) probe was designed and optimized. The probe minimizes distortion by employing low-inductance paths, coaxial geometry, and electromagnetic shielding. Its behavior was evaluated through electromagnetic simulations in CST Microwave Studio and circuit-level analysis in MATLAB, under both air and SF₆ gas environments. Key performance aspects such as rise time, bandwidth, frequency response, and linearity were assessed in detail. Results show that the probe can measure sub-nanosecond rise times with high linearity across a wide voltage range. Compared with commercial alternatives, the proposed design provides a more affordable yet equally precise solution. This makes it highly suitable for scientific research, industrial diagnostics, and medical applications requiring real-time monitoring of high-voltage transients.