Consider the propositions P and "Plausibly, P". An argument for P is not necessarily an argument for "Plausibly, P". For there might be successful arguments for counterintuitive or implausible propositions. In such cases the argument supports P but it doesn't support P being plausibly true. An argument for the proposition "Plausibly, P" is not necessarily an argument for P either. For why should in general plausibility be truth-conducive? That is, why should in general what is plausibly true for human beings be sufficiently likely actually true?
The propositions P and "Plausibly, P" are quite different propositions indeed. The first asserts that the state of affairs denoted by P obtains. The second asserts that the world is such that it is plausible that P is true. This second proposition might be true while at the same time P is false. Also P might be true whereas it is not plausible that P is true.
If we switch - in light of my 'world-for-us' theory of knowledge - the context from how the world is in itself to how the world is for us, i.e. from the-world-in-itself to the-world-for-us, the above picture changes. Within the context of the-world-for-us an argument for the proposition "Plausibly, P" is also an argument for P because within the-world-for-us plausibility is truth-conducive. Yet, within the-world-for-us an argument for P is still not necessarily an argument for "Plausibly, P". For there might be good arguments for counterintuitive or implausible truths within the-world-for-us.
Now consider the propositions P and "Likely, P". Here 'likely' is not to be equated with 'plausibly'. Plausibility refers to being in accordance with our human intuitions. Being likely though refers to having statistically a high chance or high probability of being true. These notions are not the same.
An argument for "Likely, P" is an argument for P having a high chance of being true. But then such an argument is also an argument for P. Yet, an argument for P is not necessarly also an argument for "Likely, P". For even though a successful argument for P increases the likelihood of P, it does not follow that the increase is significant enough to render P likely true.
With respect to the concept of 'likelihood' the picture does not change if we switch again from the context of how the world is in itself to how the world is for us. In both cases the conclusions remain the same.