An electron beam probe (EBP) is a detector which makes use of a low-intensity and low-energy electron beam to measure the transverse profile, bunch shape, beam neutralization and beam wake field of an intense beam with small dimensions. While it can be applied to many aspects, we limit our analysis to beam distribution reconstruction. This kind of detector is almost non-interceptive for all of the beam and does not disturb the machine environment. In this paper, we present the theoretical aspects behind this technique for beam distribution measurement and some simulation results of the detector involved. First, a method to obtain a parallel electron beam is introduced and a simulation code is developed. An EBP as a profile monitor for dense beams is then simulated using the fast scan method for various target beam profiles, including KV distribution, waterbag distribution, parabolic distribution, Gaussian distribution and halo distribution. Profile reconstruction from the deflected electron beam trajectory is implemented and compared with the actual profile, and the expected agreement is achieved. Furthermore, as well as fast scan, a slow scan, i.e. step-by-step scan, is considered, which lowers the requirement for hardware, i.e. Radio Frequency deflector. We calculate the three-dimensional electric field of a Gaussian distribution and simulate the electron motion in this field. In addition, a fast scan along the target beam direction and slow scan across the beam are also presented, and can provide a measurement of longitudinal distribution as well as transverse profile simultaneously. As an example, simulation results for the China Accelerator Driven Sub-critical System (CADS) and High Intensity Heavy Ion Accelerator Facility (HIAF) are given. Finally, a potential system design for an EBP is described.