Essentially EA tells not "let's save as many lives as possible" but "let's improve the world according to our values as much as possible". And values might differ among the people.
In your example with cure for relative working with only X probability Vs definitely curing stranger on the other side of the world there should be value X for which you will prefer to cure the stranger. Whether it 10% , 1% or maybe 0.01% I will not blame you. But it worth to know your values like value of your family member life over the stranger's life to act accordingly.
Dive into EA activities starts with exploring your values. How do you value lives of animals in comparison to lives of people? Do you prefer improving people well being now or reducing existential risks like wars and epidemies? EA literally made a tool to estimate one's values and promote this tool on the front page.