I'm trying to create a graph that shows the probability of a song reaching the top 10 of the Billboard Hot 100 over time (weeks in chart). When a song enters the chart, the probability should be something like 0.15, which would decline every week that comes next. Hence the chart should be a declining curve starting at 0.15, with x (weeks in chart) and y (probability of reaching the top 10).
1) Can I use a Kaplan-Meier curve to do this?
2) How can I create a Kaplan-Meier curve in R (survival package) that does not start at a probability of 1?
This is an interesting question. I think maybe stats.stackexchange.com will have more to say about it.
I don't think this is analogous to survival and therefore I think Kaplan-Meier or any other survival estimators won't do what you are looking for.
This is a time-to-event problem of a kind; a web search for that term might turn up some resources. But it's not a survival or reliability problem because the event in question doesn't eventually happen to all subjects (as death or mechanical failure does). In fact the event in question is pretty rare.
My advice is just bite the bullet and compute the probabilities yourself, by counting songs which reach the top 10. The basic statement you mentioned is just computing p[k] = m[k]/n[k] where for convenience I've defined m[k] = (number of songs which stayed on chart at least k weeks and eventually reached top 10) and n[k] = (number of songs which stayed on chart at least k weeks). I think p[k] is not necessarily monotonic in k -- I wouldn't be surprised if there is a bump in there. Something to look for, anyway.
Songs which fall off the chart and go back onto it kind of mess up the picture a little. My advice is to treat them as if they were on the chart the whole time. But you might very well have a different idea about how to handle them.
I can see an interesting variation. How about p[j, k] = (proportion of songs which eventually reach top 10 after at least k weeks on chart and current chart position is j) ? or how about the same, but for the initial position is j? No doubt there are others.
Good luck and have fun.