What do you do when your favourite professional road cyclists get caught out for doping?

You left out an option. What if I don't have a favorite (or favourite) professional road cyclist? What if I'd rather go watch local (amateur) racers in what's called a criterium, or crit race. https://usacrits.com/about/what-is-a-criterium/

What if my favorite cyclists competed in the 40 + and 50 + divisions. A friend of mine is SIXTY-THREE and still competes. 💪 He does quite well too. Name withheld for obvious reasons - but pic below. Also a link to a video. Rather than just getting one chance to watch 'em...they compete on closed loop circuit passing by again & again. Starting with the juniors & working up to CAT 1 racing, the competition last all day.

Video... https://vimeo.com/200925351

I would never deny anything that I thought of as ”truth”. That seems beyond pointless.
I might not agree with something I thought of as improbable or unlikely though, which is a different thing.
Apart from that, I’m not heavily enough invested in any pro rider to be particularly upset.
I’ll hold off judgement and listen to their excuses and see if/how credible they seem.
If it’s a rider that seems likeable I’d be a bit disappointed. If it’s a rider that seems cocky and obnoxious, it affects me less as it’ll seem like more in character.
Then, I’ll get on with life. If a GC rider is caught, I might be curious to see what the team does, what the race organization does and what the other teams will do. A GC rider dropping out at late stage can open up the game quite a bit.

Since I'm my favourite cyclist, I don't have that problem.

Nothing as it is extremely rare these days.

I don t have a favorite doper, so him getting caught wouldn t bother me at all.

If I’m Jerry I spend an hour on Grindr and give in to temptation

I excuse them as I know their competition does it too, they just haven't been caught yet.

It's a while since it's happened but once their reputation has been tarnished with using drugs I never really have the same enthusiasm for them. After Alejandro Valverde served a doping ban I felt his subsequent achievements didn't mean much.