Knowing is one thing, and proving something is another...
Evidence is experience based... Perhaps the only knowledge is 'Self-Knowledge'...
You can get the impression from someone that they've proved it to themselves, but this 'proof' is not independent of your own understanding....
I guess this is why so many people talk about, recommend, use, and support the idea, that, all you need to do is to 'prove it to yourself', or to 'see it for yourself'...
In such strong feelings like love... You've got such a strong feeling that is almost shared, an experience almost shared, a proof that is almost shared... There's just so much in the kind of feeling that is shared and, perhaps love is the greatest of these kind of feelings... Hard to deceived at a time like this...
Mistrust is a greatly contrasting feeling to love.
Mistrust is there until you've seen it for yourself, only weakened by the strong feeling(s) you get that the other person(s) (making the claim) has seen it for themselves, or you've gone through something similar before...
As to 'contrasting possibilities in equilibrium'...
You will always have a degree of mistrust, and a degree of love for all things, due to a degree of self-doubt and a degree of hope for all situations. To always see 'a way a thing could work'... Possibilities...
There is an inherent contrast of love and mistrust, simply more profound when they are in equilibrium. The profundity subsides toward the 'absolute' when you have worked 'enough' with the 'idea of contrast'... When you have developed belief...
As to being typically loving or mistrustful...
The judging and belief systems, as tools, will point someone closer to or further from the truth depending on how reliable they are...
However, it's not just the 'tools' we use, it's the state we're in to be able to make the best use of those tools...
Just think of the drug-addicted person at their different stages... From just trying it, to getting serious, to trying to quit, to getting serious again, and finally giving up... Not much changes in the tool 'drugs are bad, m'okay', but through experience, belief, and mental states, they can finally get to 'drugs are bad for me, m'okay'...
As to knowledge being the ultimate power or the ultimate deception...
There is a quote 'Knowledge is power, and knowledge can mean the difference between life and death...'
I don't see how something, made so true by proof, can be deceiving, unless the knowledge was too much based on trust alone, rather than solely from one's experience with the situation at hand...
As to 'Can we truly know what so many people have accepted as fact or at the least have considered the most probable answer, or is any possibility actually as likely as any other?'
If you spend enough time, in a clear mind on something, it will be apparent what your feelings are in regards to whether you have seen it for yourself. True knowledge will come from there...
The idea of 'odds' (like for betting) is what you get to when you think of likelihoods...
To summarise 'odds', although it may be rare or unlikely, you may just happen to come across any of the options in the situation at hand...
In so, you often have a feeling that anything can happen, this is only dampened when belief comes in to play. Eliminating belief eliminates any betting from occurring...
If you have a strong enough belief, from a strong enough 'self-evident' understanding, you're betting or optioning becomes more orientated to knowledge. If this involves another person, maybe their body language, vocal inflexions, or other 'tells' would show their experience in regards to the situation...
Sorry for the lengthy response, I hope I didn't miss the points...