TeX source:

𝑃(t_4| t_3 t_5) = \frac{𝑃(t_4 t_5|  t_3)}{𝑃(t_5|  t_3 )}=\frac{𝑃(t_4 |  t_3)𝑃(t_5| t_3 t_4)}{\sum_t 𝑃(T_4=t, t_5|  t_3)}=\frac{𝑃(t_4 | t_3)𝑃(t_5| t_4)}{\sum_t 𝑃(T_4=t | t_3)𝑃(t_5| T_4=t)}