Multiple Feeders, One Single Optimized Antenna

So, I wanna mount a single Gucci expensive antenna on my roof, and somehow get the coax down to my livingroom where my 3 feeders live comfortably humming along. What I DON'T wanna do is mount three Gucci expensive antenna on my roof, and somehow get three coax cables down to my livingroom where my 3 feeders live comfortably humming along.

I am pretty good with the math, and based on my comprehensive analysis and calculations, doing the latter would require 2.5 times the effort, cost, and risk of falling off and breaking body bits. So I want to cheat by making the three feeders share one antenna. I am planning on lying to them to avoid the crying and whining about wanting their own, which should work for that, but I need to make sure they don't realize they are all suckling the same teet due to some implications doing so would have on the signals they are being fed.

I don't know enough to say what this would be, nor do I know what I could do to prevent the things I don't know about. However, every once in awhile, I guess correctly and can act like I knew it the whole time. So lets give it a go!

I believe that splitting the coax twice to achieve 3 separate coax connections would cause the standard 50 ohm impedance that the SDRs are happiest with to become something not 50 ohms, thus making the SDRs something other than happy. My intuition tells me that when you have a signal with X power, splitting the the cable the signal is propagating into 3 separate cables results in each cable now providing the signal at 1/3X power. However, I am smart enough to know that calculations in any discipline related to the electromagnetic spectrum are rarely that simple, and it's almost never a zero sum game which that theory is predicated on.

I don't know enough about the characteristics of analog carrier waves to say for certain, but I have to think that nothing is free, and whether or not it's as simple as dividing by 3 or not, doing so will result in some significant signal degradation for all three receivers.

I know there is an ohm's law, but I don't know what it is, or whether or not it applies here. Ohms, the unit of measurement for resistance, I would expect the resistance to drop because there are now 2 additional paths for the same signal. That assumes that electrons and water travel in the exact same way, and while often used to compare the two unrelated disciplines of science, I know that to be false.

So the degradation of signal is a no brainer, an LSA should mitigate the low power issue, but is it a single amplifier? If it's single, I would expect that the base of the antenna is ideal. Is it 3 LSAs, one for each of the 3 coax cables feeder the feeders who are feeding om their feed? If so, do they go just after the splits? Also, would putting 3 LSAs in that, or more ideal configuration do anything for my increase/ decrease in ohms that I posited would occur? If the answer is a single LSA at the antenna base, I don't see that helping the ohm's implications occurring at the coax splits further down stream, so would there be another way to address that? Do I over think things and try to dissect a problem by asking a hundred scenario-based questions when asking a simple how-to question would be more efficient way to get an answer and avoid confusing people?

I'm excited to hear because I bet....I BET that having that Gucci antenna on the roof will be a little better than the 3 flat $8.00 antennas I currently have taped to the windows in my livingroom right now. Thanks for reading my quick short-story, and giving me some education.

Also, if anyone is aware of an online, free, below Phd-level resource on the interwebs that I could use to educate myself on all the intricacies and variables which go into antenna signal optimization, tuning, design variables, performance metrics, how those metrics are manipulated, and what metrics are associated with which performance variables, could you drop it in a reply and press POST. That way I won't have to ask all them questions here!!!!

Thanks yo's! I'm trying to be less dumb everyday, and you guys are the ones who I turn to cause the answers are always on point!