Eevee is not great at global illumination and bounce lighting, for light to be calculated on those tight spots Cycles is what will get the job done. If you want to stick to Eevee then you have to use light probes to calculate and bake the shadow information or you can also use raytracing of course. Things may have changed a little when using probes lately, so you should watch the Fundamentals of lighting if you haven’t already. Here’s one of the lessons that will give you a quick understanding:
https://cgcookie.com/lessons/baked-light-with-irradiance-volumes
