We study theoretically the properties of a three-photon state prepared inside a semiconductor cavity, due to the interaction between a quantum dot and an electromagnetic field, and two consecutive spontaneous parametric downconversion (SPDC) processes. Thus, we consider a scheme involving three modes of the electromagnetic field, whose frequencies are given by the SPDC processes: $\omega_0 \rightarrow \omega_1 + \omega_2$, and $\omega_2 \rightarrow \omega_1 + \omega_1$. Furthermore, we study the low excitation regime, in which a three-photon state is accessible within the system's dynamics.