How could you calculate the probability of an event that we have no idea about? We don't even know for sure that life originated entirely on earth itself - life or some crucial substances required for it could have originated on some other planet with conditions we know nothing about and been brought to earth on some meteorite; or it could have originated in some extreme conditions like a comet tail in close proximity to the sun.

I'm not saying these are necessarily plausible theories, but the fact that we can't discount them tells me enough about how likely we are to be able to calculate a probability for abiogenesis.

Life seeded implies that life still went through abiogenesis somewhere else.

I agree that we can't know the exact means, just that abiogenesis happened, but we can still calculate the probability of our conditions needing to occur for abiogenesis to happen.

Of course abiogenesis had to occur somewhere, but if we can't be sure that abiogenesis occurred on Earth itself, it means we don't have any clear idea yet of the conditions necessary for abiogenesis (apart from some a priori knowledge, such as needing to have carbon and water). Perhaps the necessary conditions are extremely strange.

We already know that Earth as it is today can't support abiogenesis, since it's not happening, and judging from the phylogenetic tree, it probably hasn't happened for more than 3 billion years. There is also a reason to believe that even if the Earth was once appropriate for abiogenesis, it only happened once, given that all life on Earth shares the same chemistry (though of course it is possible that there was simply no other way for life to be, or that there have existed other forms of life from other abiogenesis events, but that they simply have not survived).

The assumptions probably dictate the probability more than anything else.

We don't even know how life originated on Earth

Abiogenesis implies natural means, but I agree that we simply do not know.