How to calculate the influence on load bearing on beams cut/notched for connections?
You're overlooking a couple of important factors, starting with deflection. Smaller structural members will flex more than thicker ones, especially in the middle of the span. Sag also adds lateral loads to the connections at the end since it they must resist the pull of the shorter curved member. 

Those connections are the second thing you've overlooked. You do need to fasten things together eventually and butt joinery puts all of the load on the fasteners. Generally two thirds of a beam is quite a bit stronger than two or three nails. It's worth noting that it's fairly common to use angle iron and bolts when the work will be covered up. 

I suspect that notching wooden members in new construction is pretty much limited to timber frame buildings. It's getting harder to find solid wood beams than it used to be, and modern structural joinery tends to incorporate steel fasteners to protect against extreme weather events. For hurricanes or tornadoes you want the joint tied down; for earthquakes you want it to deform rather than snap. 

Getting back to your original question, structural engineers have access to lots of data to work on the estimate. They can look up the strength of a given material, average weight of a building per story, strength of a given joint compared, etc. From there it's fairly straightforward physics.

Simulation is also a common tool. Once the plans are drawn in CAD you can specify the building and wind loads and get a detailed report on the expected performance. If you're really, really interested Autodesk Fusion 360 is free for hobby use and will let you run some simulations. You'd have to deal with the learning curve and it's not the right tool to design a building, but it'll do for mucking about with simple joints. (Alternately you might find just the tutorial video on simulation entertaining.)

Non-engineers generally rely on experience and rules of thumb (or the building code in these more enlightened times) and gratuitous over-building. Nobody would notch anything as small as you've got in your sketch. In the US they wouldn't be called "beams" either as they're too small. Joists would be at least 150mm thick and wooden beams 200mm or more.