The probability of a lightning downstrike starting a fire depends on if the strike has a component called a continuing current. This was news to me until I read it on the Wildland Fire Assessment System site. I knew that positive strikes were more likely to start a fire than a negative strike, but now I know why that happens.
All positive strikes have continuing current, but only 20% of negative strikes do. The probability of a downstrike starting a fire depends on if it has continuing current (or the duration of the current) and how receptive the fuel is to igniting, with fuel moisture playing a prominent role.
Regarding the map above, the WFAS says:
The ignition efficiency on a 1 km pixel is given on a per discharge basis. That is, if the efficiency is high, then about 9 discharges will result in one ignition; if the efficiency is extreme, about 5 or fewer discharges will result in an ignition. The ratio of positive and negative discharges is built into the calculation. (Latham and Schlieter 1989) document the algorithm.