A useful paradigm for this is to think about a deck of cards. Shuffle it up, and draw one. What is the probability that the top card is black?
A logical interpretation of this would be to say "Okay, what is the state space of the possible state of the cards, and in what proportion of that space do we say that the top card is black?". You look at the 52 cards, you spot that the space splits neatly into 26 of each colour, and in the understanding that the deck has been properly randomised you conclude that "The probability is 0.5, because that is the proportion of the state space that is black"
Ahh, says Ramsey, hold on a second. This idea of being 'properly randomised' begs the very question at work here. We constructed a model of the deck of cards on the basis of the evidence observed. The 'relation' of probability at work in any given card draw isn't just pure mathematics, but also depends on features outside the model, such as whether the deck is stacked, whether any cards are duplicates, whether the dealer is using sleight of hand and so on.
Logical models of probability give us a very useful framework for how to distribute our estimates effectively, but they're not the whole or even a strictly necessary part of the story. It can even result in inappropriate attributions of confidence, in that most people using probability estimates do not generally give good evidence for the models being used to assess the probabilities of individual events they predict.
Ramsey, as a subjectivist, would argue that we make our judgements of probability on the basis of confidence, not on a mechanical statement of known facts.
However, his opponent ought not, strictly speaking, be said to be presenting an account of the "objective metaphysical chance" of the top card in our example being black. Why not? Well, having shuffled the deck of cards, a mechanical process which puts the sequence of cards in some order, the top card of the deck is now fixed.
If you freeze time at the point at which the shuffle is finished, and consider various branching futures from this point which vary only in accordance with the laws of physical possibility, you are not now going to find some possible futures where the card is black and some where the card is red. That is, the objective metaphysical chance that the card on top is black can have exactly one of two values - 0 or 1.
In fact, this is the same objective metaphysical chance as that of the top card being exactly the 9 of diamonds - it either is, or it isn't. We aren't currently in a position of any kind of metaphysical flux - the shuffle has concluded, the deck is in some sequential order, and all that remains is for us to find out what that order is.
This more metaphysical concept of chance does have some relevance in Physics, in that some of our Quantum Physical models potentially have an element of indeterminacy written into their known principles. But this isn't generally what people talk about when they refer to the logical model of probability as objective - what they mean, rather, is a more epistemic point, that the parameters of a model of assigning probabilities to events can be determined independently of the beliefs of any observers involved.