You can do this with the Light Path Shader Node.
EDIT: Do note that I what I posted works with the default settings in cycles, but EVEE reflections behave differently so it might not be the exact same.
Here is a basic shader setup that prevents reflective surfaces from seeing your object. In fact it prevents it from casting any reflected light at all.
You can turn this
By using this Shader setup Involving the afformentioned Light Path Node.
You can read more about the Light Path Node here but the value you are interested in is the "Is Reflection" value.
Long story short, things that have light reaching you only as a result of reflection from other objects (in this case the underside of the ball) are flagged as "reflection" rays by this light path.
This shader setup works by using the mix and transparent shader nodes, driven by the light path. If a ray is a reflected light path, it has a value of 1 being put into the FAC value of the mix shader. This makes the mix shader choose 100% of the SECOND input shader.
Non reflected light gets classified with a 0 in FAC therefore it only chooses 100% of the FIRST input of the mix shader
You can use this effect to for example, make reflections semi transparent if you replaced the second node with a translucent shader instead of a transparent one or you can put a complicated node graph to use in place of the reflection while leaving the original directly viewed object as its normal shader.
This is especially interesting if you plan to do NPR (Non photo real) renders etc.