The probability meaning of Covid variants

The studies referenced do not have any such specifics about transmission probability.

What they observe is that a variant is becoming more common. Modeling the spread gives a different R₀ value for the variants vs the reference strains:

In line with previous modelling studies, the R0 for VOC-202012/01 was estimated as 75% more transmissible than other variants [35]. Davies et al. modelled data from three English regions to estimate that VOC 202012/01 is 56% more transmissible (95% credible interval (CrI): 50-74%) than previously identified SARS-CoV-2 variants [32]. Danish modelling studies performed in January 2021 estimated that VOC 202012/01 was 36% more transmissible than other variants [ECDC communication with Danish authorities].

(from your second reference)

They infer that the variant is more transmissible because the modeled number of people subsequently infected per infected person is greater. The reasons for this cannot be easily determined by the methodology they refer to, and there is no simple way to map this onto probability of infection given some exposure; they are just describing what happens in real-world conditions, on average.

What you can infer is that there are some types of contact that occur in the real world that wouldn't result in transmission with the old strain that do result in transmission of the variant. This could be because more infected people produce enough virus to spread to others, it could be because shorter contacts lead to infection, it could be because infected people have different behavior that leads to more contact with people to potentially get infected; you can't tell the difference from these data.