A transient plasma medium is generated by a plume laser interaction with solid. This system is considered as a very useful pulse charge source. Previous experimental studies, provided measurements of the potential using floating probe system of different geometry. There is draw back experimental since it allows to measure the potential changes at specific locations. The temporal and the spatial changes into plasma parameters are necessary for all the absorption and emission calculation. In this work, we have collected these data and implement it numerically to provide the following: 1. The potential and charge density in 2D space for different times. 2. The potential, charge density, number of electron and temperature in 1D space for all the pulse period. The spatial and temporal behavior of the resulted parameters reflected the complexity at this system, and demonstrated that the floating probe method have the potential to provide the necessary information for the plasma produced by laser.